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.

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Found problems: 4

2017 China Team Selection Test, 4
Tags: kobayashi , number theory
Given integer $d>1,m$,prove that there exists integer $k>l>0$, such that $$(2^{2^k}+d,2^{2^l}+d)>m.$$

STEMS 2021 Math Cat B, Q2
Tags: polynomial , power of 2 , prime number , divisibility , kobayashi
Determine all non-constant monic polynomials $P(x)$ with integer coefficients such that no prime $p>10^{100}$ divides any number of the form $P(2^n)$

2017 China Team Selection Test, 4
Tags: number theory , kobayashi
Given integer $d>1,m$,prove that there exists integer $k>l>0$, such that $$(2^{2^k}+d,2^{2^l}+d)>m.$$

2019 Iran MO (3rd Round), 3
Tags: number theory , kobayashi
Let $S$ be an infinite set of positive integers and define: $T=\{ x+y|x,y \in S , x \neq y \} $ Suppose that there are only finite primes $p$ so that: 1.$p \equiv 1 \pmod 4$ 2.There exists a positive integer $s$ so that $p|s,s \in T$. Prove that there are infinity many primes that divide at least one term of $S$.