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

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 2

2000 BAMO, 1
Tags: relative prime , sum , number theory
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.)

2012 BAMO, 5
Tags: relative prime , polynomial , integer polynomial
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.)