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: 7

2023 Belarus Team Selection Test, 2.1
Tags: number theory , divsibility , primes
Find all positive integers $n>2$ such that $$ n! \mid \prod_{ p<q\le n, p,q \, \text{primes}} (p+q)$$

2022 IMO Shortlist, N2
Tags: number theory , divsibility , primes
Find all positive integers $n>2$ such that $$ n! \mid \prod_{ p<q\le n, p,q \, \text{primes}} (p+q)$$

2023 Indonesia TST, 1
Tags: number theory , divsibility , primes
Find all positive integers $n>2$ such that $$ n! \mid \prod_{ p<q\le n, p,q \, \text{primes}} (p+q)$$

2023 Germany Team Selection Test, 1
Tags: number theory , divsibility , primes
Find all positive integers $n>2$ such that $$ n! \mid \prod_{ p<q\le n, p,q \, \text{primes}} (p+q)$$

2023 Indonesia TST, 1
Tags: number theory , divsibility , primes
Find all positive integers $n>2$ such that $$ n! \mid \prod_{ p<q\le n, p,q \, \text{primes}} (p+q)$$

2023 Thailand TST, 1
Tags: number theory , divsibility , primes
Find all positive integers $n>2$ such that $$ n! \mid \prod_{ p<q\le n, p,q \, \text{primes}} (p+q)$$

2023 Switzerland - Final Round, 6
Tags: number theory , divsibility , primes
Find all positive integers $n>2$ such that $$ n! \mid \prod_{ p<q\le n, p,q \, \text{primes}} (p+q)$$