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

Source: 2020 Argentina OMA L3 p4

December 26, 2020

primeIntegernumber theory

Problem Statement

Let

a

and

b

be positive integers such that

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

is an integer. Show that

a

is not prime.