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a = n^5 + 6n^3 + 8n ¸ b = n^4 + 4n^2 + 3 are relative prime of have gcd 3

Source: 2002 Moldova JBMO TST p1

February 25, 2021
number theorygreatest common divisor

Problem Statement

For any integer nn we define the numbers a=n5+6n3+8na = n^5 + 6n^3 + 8n ¸ b=n4+4n2+3b = n^4 + 4n^2 + 3. Prove that the numbers aa and bb are relatively prime or have the greatest common factor of 33.
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