
803 P.2d 187 (1990)
The PEOPLE of the State of Colorado, In the Interest of J.M.A., Child.
Upon the Petition of Jefferson County Department of Social Services and K.A.A., Petitioners/Appellees, and
Concerning P.L., Respondent/Appellant.
No. 90SA117.
Supreme Court of Colorado, En Banc.
December 17, 1990.
*188 G.E. Shields, Lakewood, for petitioner/appellee Jefferson County Dept. of Social Services.
Cipriano Griego, Winzenburg, Leff, Mitchell and Wein, Lawrence B. Leff, Denver, for respondent/appellant.
Justice VOLLACK delivered the Opinion of the Court.
The respondent P.L. appeals the trial court holding that section 19-6-108, 8 C.R.S. (1977), is unconstitutional as it denies the equal protection of the laws to children with no presumed fathers, in violation of the fourteenth amendment to the United States Constitution, and granted summary judgment in favor of Jefferson County Department of Social Services (the Department) and K.A.A. We affirm.

I.
K.A.A. gave birth to J.M.A. on February 16, 1982. J.M.A.'s birth certificate did not give the name of his father. In April 1982, K.A.A. applied for Aid to Families with Dependent Children (AFDC) in Boulder County. She was found eligible and received these benefits from April 1982 through May 1983. K.A.A. and J.M.A. moved to Jefferson County and applied for AFDC benefits. K.A.A. received benefits from Jefferson County beginning in December 1983 and continuing through March 1989.
On August 16, 1988, the Department filed a verified petition for determination of a parent-child relationship in the Jefferson County District Court. P.L. was served with the verified petition and a summons on August 27, 1988. On September 2, 1988, P.L. appeared pro se and entered into a stipulation with the Department. The stipulation provided that P.L. submit to a blood test and HLA tissue-typing analysis *189 to be performed by Genetic Design, Inc., a private blood-testing company. Blood samples were taken from P.L., K.A.A., and J.M.A. on September 6, 1988. The report filed with the court indicated a 99.79% probability that P.L. was J.M.A.'s biological father.
On October 17, 1988, P.L. appeared pro se and verbally denied paternity of J.M.A. The court ordered P.L. to file a written response to the petition in paternity on or before October 28, 1988. P.L. requested that the court order a second blood test. In its order, the court stated that it would consider ordering a second blood test if P.L. alleged a good-faith argument that the first test was defective in some way. P.L. retained counsel to represent him in the remainder of these proceedings. P.L.'s counsel prepared a written response but did not allege any defect in the first test, and a second test was not ordered.
P.L.'s response also failed to allege any substantive defense such as non-access or impotency. The response consisted solely of a general denial to the verified petition of paternity. The Department, relying on the results of the blood test, filed a motion for summary judgment on the issues of paternity and duty to support. On February 24, 1989, P.L. filed a motion to dismiss based on the statute of limitations. On March 9, 1989, P.L. filed a brief in opposition to the motion for summary judgment. The brief was submitted without any accompanying affidavits or other evidence to support P.L.'s position.
The trial court granted the Department's motion for summary judgment on March 13, 1989, based on P.L.'s failure to show by affidavit or otherwise that there were any material issues of fact with regard to paternity. The court, on March 16, 1989, heard arguments concerning P.L.'s motion to dismiss. P.L. argued that the statute of limitations in effect at J.M.A.'s birth barred the bringing of paternity actions three years after the birth of the child. The Department responded by arguing that section 19-6-108 was unconstitutional because it unfairly discriminated against children with no presumed father by placing time limits on establishing paternity.
The trial court, in denying P.L.'s motion to dismiss, ruled that section 19-6-108 was unconstitutional because it violated the fourteenth amendment of the United States Constitution by denying equal protection of the law to children without presumed fathers.

II.
P.L. first contends that the trial court erred in ruling that section 19-6-108[1] was unconstitutional because it denied equal protection of the law to children without presumed fathers. P.L. argues that the trial court's reliance on Clark v. Jeter, 486 U.S. 456, 108 S.Ct. 1910, 100 L.Ed.2d 465 (1988), in reaching this conclusion was misplaced. We disagree.

A.
In determining whether state legislation violates the equal protection clause of the fourteenth amendment, U.S. Const. amend. XIV, § 1, the United States Supreme Court utilizes varying degrees of scrutiny, depending on the type of classification employed by the statute. The Court applies an intermediate level of scrutiny to discriminatory classifications based on illegitimacy. See Jeter, 108 S.Ct. at 1914; Pickett v. *190 Brown, 462 U.S. 1, 8, 103 S.Ct. 2199, 2204, 76 L.Ed.2d 372 (1983); Mills v. Habluetzel, 456 U.S. 91, 99, 102 S.Ct. 1549, 1554, 71 L.Ed.2d 770 (1982). The Court has interpreted this intermediate-level-of-scrutiny standard to mean that classifications based on illegitimacy are invalid unless they are "substantially related to a legitimate state interest." See Mills, 456 U.S. at 99, 102 S.Ct. at 1554; United States v. Clark, 445 U.S. 23, 27, 100 S.Ct. 895, 899, 63 L.Ed.2d 171 (1980); Lalli v. Lalli, 439 U.S. 259, 265, 99 S.Ct. 518, 523, 58 L.Ed.2d 503 (1978). The Court has recognized that in some circumstances the state may treat illegitimate children differently because of "lurking problems with respect to proof of paternity." Jeter, 108 S.Ct. at 1914, (quoting Gomez v. Perez, 409 U.S. 535, 538, 93 S.Ct. 872, 875, 35 L.Ed.2d 56 (1973).
The United States Supreme Court has applied this intermediate level of scrutiny to a series of cases dealing with equal-protection challenges to statutes of limitations that apply to paternity suits. In the first case of the series, Mills v. Habluetzel, 456 U.S. 91, 102 S.Ct. 1549, 71 L.Ed.2d 770 (1982), the Court developed a two-part test for evaluating equal-protection challenges to statutes of limitations concerning paternity suits.
First, the period for obtaining support... must be sufficiently long in duration to present a reasonable opportunity for those with an interest in such children to assert claims on their behalf. Second, any time limitation placed on that opportunity must be substantially related to the State's interest in avoiding the litigation of stale or fraudulent claims.
Id. at 99-100, 102 S.Ct. at 1554-55.
The Court in Mills found that the Texas one-year statute of limitations failed both parts of the test. The one-year period was deemed inadequate to provide illegitimate children with the opportunity to obtain paternal support. The Court also found that the one-year period was not substantially related to a legitimate state interest.[2]
The next case in the series is Pickett v. Brown, 462 U.S. 1, 103 S.Ct. 2199, 76 L.Ed.2d 372 (1983). The Court applied the two-part test developed in Mills to the facts of that case and found that Tennessee's two-year statute of limitations failed both parts of the test. After applying the first part of the test, the Court concluded that "the 2-year limitations period severely restricts [an illegitimate child's] right to paternal support." Pickett, 462 U.S. at 12, 103 S.Ct. at 2206. The Court then applied the second part of the test and concluded that "the 2-year statute of limitations was not substantially related to Tennessee's asserted interest in preventing stale and fraudulent claims." Id. The Court was also persuaded by the fact that Tennessee tolled most other actions during a child's minority. Finally, the Court noted that advances in blood testing had alleviated some of the problems of proof in paternity actions. Based on this reasoning, the Court found the Tennessee two-year statute of limitations unconstitutional.
The most recent case decided by the United States Supreme Court dealing with statutes of limitations regarding paternity cases is Clark v. Jeter, 486 U.S. 456, 108 S.Ct. 1910, 100 L.Ed.2d 465 (1988). In Jeter, the Court considered the constitutionality of Pennsylvania's six-year statute of limitations. The Court held that "[e]ven six years does not necessarily provide a reasonable opportunity to assert a claim on behalf of an illegitimate child" and that "it is questionable whether a State acts reasonably when it requires most paternity and support actions to be brought within six years of an illegitimate child's birth." Id., 108 S.Ct. at 1915. In applying the second part of the test, the Court stated:
We are, however, confident that the 6-year statute of limitations is not substantially related to Pennsylvania's interest in avoiding the litigation of stale or fraudulent claims. In a number of circumstances, Pennsylvania permits the issue of paternity to be litigated more than six years after the birth of an illegitimate child. The statute itself permits a *191 suit to be brought more than six years after the child's birth if it is brought within two years of a support payment by the father. And in other types of suits, Pennsylvania places no limits on when the issue of paternity may be litigated.
Id. at 1915-16.

B.
The respondent argues that the Colorado statute of limitations is constitutionally sufficient because it provides in part that "an action brought by or on behalf of a child whose paternity has not been determined is not barred until three years after the child reaches the age of majority." § 19-6-108, 8 C.R.S. (1977). Respondent cites People in the Interest of T.L.H. v. F.P.V., 701 P.2d 87, 88 (Colo.App.1984), as support for upholding the three-year statute of limitations.
Respondent's argument is flawed because it fails to address the complete language of the statute. The first part of section 19-6-108 provides:
An action to determine the existence of the father and child relationship as to a child who has no presumed father under section 19-6-105 may not be brought later than three years after the birth of the child or later than three years after July 1, 1977, whichever is later.
This language is substantially similar to the language the United States Supreme Court found unconstitutional in Mills, Pickett, and Jeter. The Colorado three-year statute of limitations suffers from the same deficiencies as those cases. The Colorado statute of limitations fails the first part of the test because it does not "present a reasonable opportunity for those with an interest in [illegitimate children] to assert claims on their behalf." Mills, 456 U.S. at 99-100, 102 S.Ct. at 1555. Many of the practical obstacles to filing a claim for support within the first year of the child's birth are likely to continue after the first year of the child's life. Id. at 102-06, 102 S.Ct. at 1556-58 (O'Connor, J., concurring). Therefore, we conclude that the three-year period provided in section 19-6-108 does not provide an adequate opportunity for paternity and support actions to be brought on behalf of illegitimate children.
The three-year statute of limitations also fails the second part of the test set forth in Mills. The three-year limitation is not substantially related to Colorado's interest in avoiding the litigation of stale or fraudulent claims. Section 19-6-108 treats children with presumed fathers differently than children without presumed fathers.[3]
*192 The United States Supreme Court addressed a similar problem in Pickett. The Court reviewed a two-year statute of limitations that contained an exception for illegitimate children who were, or were likely to become, public charges. The exception allowed suits to be brought on behalf of these children at any time prior to the child's eighteenth birthday. In holding that the statute failed the second part of the test, the Court stated:
The exception in the statute, therefore, seriously undermines the State's argument that the different treatment accorded legitimate and illegitimate children is substantially related to the legitimate state interest in preventing the prosecution of stale or fraudulent claims and compels a conclusion that the 2-year limitations period is not substantially related to a legitimate state interest.
Pickett, 462 U.S. at 15, 103 S.Ct. at 2207.
Medical advances made in blood testing reinforce our belief that the three-year limitations period is not substantially related to the legitimate state interest in avoiding the litigation of stale or fraudulent claims. Modern blood tests have eliminated many of the proof problems associated with determining paternity and can accurately determine the paternity of a child years after the child is born. See People in the Interest of M.P.R., 723 P.2d 743, 745 (Colo.App. 1986); E.M.F. v. N.N., 717 P.2d 961, 962-64 (Colo.App.1985). The Court in Jeter accepted this argument and stated that "it is an additional reason to doubt that Pennsylvania had a substantial reason for limiting the time within which paternity and support actions could be brought." 108 S.Ct. at 1916.
We conclude that the three-year limitations period contained in section 19-6-108 does not provide children without presumed fathers an adequate period of time to determine paternity or obtain support. We also conclude that this limitation is not substantially related to the state's legitimate interest in avoiding stale or fraudulent claims. Section 19-6-108 therefore violates the equal protection clause.

III.
Respondent next contends that the trial court erred in granting the Department's motion for summary judgment. Respondent argues that the blood test results relied upon by the Department were insufficient to support a grant of summary judgment. Respondent also argues that genuine issues of material fact existed even in light of the test results. We disagree.
Under Colorado law, if the blood tests show that there is a 97% or greater chance that the alleged parent is the parent, then the results must be admitted as evidence. Section 13-25-126(1)(e)(IV), 6A C.R.S. (1987), provides:
If the experts conclude that the blood tests show that the alleged parent is not excluded and that the probability of the alleged parent's parentage is ninety-seven percent or higher, the alleged parent is presumed to be the parent, and this evidence must be admitted.
If a party has an objection to the test results, then the objection must be made in accordance with section 13-25-126(1)(d), 6A C.R.S. (1987), which provides that "[a]n objection to the tests performed on the blood or tissue specimens taken pursuant to this section, or the results thereof, shall be made prior to trial." (Emphasis added).
In this case, the blood test results indicated a 99.79% probability of P.L. being J.M.A.'s biological father. P.L. received a copy of the test results prior to the hearing on the Department's motion for summary judgment, and did not object to the admission of the test results as required by section 13-25-126(1)(d). P.L.'s failure to object resulted in the admission of the test results under section 13-25-126(1)(e)(IV). The Department then moved for summary judgment based on the blood test results. Once the Department met its initial burden *193 of production, the burden shifted to P.L. to establish that there was a triable issue of fact. Churchey v. Adolf Coors Co., 759 P.2d 1336, 1340 (Colo.1988); Continental Airlines v. Keenan, 731 P.2d 708, 713 (Colo.1987). P.L. filed a brief in opposition to the motion for summary judgment which contained a general denial and was not supported by affidavits or other evidence establishing that there were genuine issues of fact. C.R.C.P. 56(e) states in relevant part:
When a motion for summary judgment is made and supported in this Rule, an adverse party may not rest upon the mere allegations or denials of his pleading, but must set forth specific facts showing that there is a genuine issue for trial. If he does not respond, summary judgment, if appropriate, shall be entered against him.
P.L. rested on the general denial contained in his answer and did not demonstrate by relevant and specific facts that a real controversy existed with regard to his paternity. McLaughlin v. Allen, 689 P.2d 1169, 1171 (Colo.App.1984). A genuine issue of fact cannot be raised simply by means of argument by counsel. Sullivan v. Davis, 172 Colo. 490, 495, 474 P.2d 218, 221 (1970). P.L.'s failure to meet his burden of production demonstrated that there were no genuine issues of material fact. Therefore, summary judgment was properly entered in favor of the Department. Morlan v. Durland, 127 Colo. 5, 10, 252 P.2d 98, 100 (1952).
Judgment affirmed.
NOTES
[1]  The version of § 19-6-108, 8 C.R.S. (1977), in effect in 1982 provided:

An action to determine the existence of the father and child relationship as to a child who has no presumed father under section 19-6-105 may not be brought later than three years after the birth of the child or later than three years after July 1, 1977, whichever is later. However, an action brought by or on behalf of a child whose paternity has not been determined is not barred until three years after the child reaches the age of majority. This section and section 19-6-107 do not extend the time within which a right of inheritance or a right to a succession may be asserted beyond the time provided by law relating to distribution and closing of decedents' estates or to the determination of heirship, or otherwise.
Section 19-6-108 was amended in 1985 and 1986. In 1987, it was repealed and reenacted as § 19-4-108. It was amended again in 1987, 1988, and 1989. We consider only the version of the statute in effect in 1982 as to the constitutional question.
[2]  In a concurring opinion, Justice O'Connor explained why statutes of limitations longer than one year may also be unconstitutional. See Mills, 456 U.S. at 102-06, 102 S.Ct. at 1556-58.
[3]  The guidelines for determining whether a presumption of paternity arises is set forth in § 19-6-105, 8 C.R.S. (1977), which, in relevant part, provides:

(1) A man is presumed to be the natural father of a child if:
(a) He and the child's natural mother are or have been married to each other and the child is born during the marriage, or within three hundred days after the marriage is terminated by death, annulment, declaration of invalidity of marriage, dissolution of marriage, or divorce or after a decree of legal separation is entered by a court;
(b) Before the child's birth, he and the child's natural mother have attempted to marry each other by a marriage solemnized in apparent compliance with law, although the attempted marriage is or could be declared invalid; and:
(I) If the attempted marriage could be declared invalid only by a court, the child is born during the attempted marriage, or within three hundred days after its termination by death, annulment, declaration of invalidity of marriage, dissolution of marriage, or divorce; or
(II) If the attempted marriage is invalid without a court order, the child is born within three hundred days after the termination of cohabitation;
(c) After the child's birth, he and the child's natural mother have married, or attempted to marry, each other by a marriage solemnized in apparent compliance with law, although the attempted marriage is or could be declared invalid; and:
(I) He has acknowledged his paternity of the child in writing filed with the court or registrar of vital statistics;
(II) With his consent, he is named as the child's father on the child's birth certificate; or
(III) He is obligated to support the child under a written voluntary promise or by court order[.]
Once a presumption of paternity arises, the time limitation for determining the father-and-child relationship is set forth in § 19-6-107, 8 C.R.S. (1977), which, in relevant part, provides:
(1) A child, his natural mother, or a man presumed to be his father under section 19-6-105(1)(a), (1)(b), or (1)(c), may bring an action:
(a) At any time for the purpose of declaring the existence of the father and child relationship presumed under section 19-6-105(1)(a), (1)(b), or (1)(c)[.]
