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a not prime if (5a^4+a^2)/(b^4+3b^2+4) is an integer

Source: 1st National Women's Contest of Mexican Mathematics Olympiad 2022 , levels 1+2 p6

September 17, 2022

number theorycomposite numberInteger

Problem Statement

Let

a

and

b

be positive integers such that

\frac{5a^4+a^2}{b^4+3b^2+4}

is an integer. Prove that

a

is not a prime number.