This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2012 BAMO, 5
Find all nonzero polynomials $P(x)$ with integers coefficients that satisfy the following property: whenever $a$ and $b$ are relatively prime integers, then $P(a)$ and $P(b)$ are relatively prime as well. Prove that your answer is correct. (Two integers are [b]relatively prime[/b] if they have no common prime factors. For example, $-70$ and $99$ are relatively prime, while $-70$ and $15$ are not relatively prime.)
relative prime integer polynomial polynomial number theory polynomials

2000 BAMO, 1
Prove that any integer greater than or equal to $7$ can be written as a sum of two relatively prime integers, both greater than 1. (Two integers are relatively prime if they share no common positive divisor other than $1$. For example, $22$ and 15 are relatively prime, and thus $37 = 22+15$ represents the number 37 in the desired way.)
relative prime number theory sum