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Complicated binomial divisibility

Source: Iran Team selection test 2024 - P9

May 19, 2024
number theory

Problem Statement

Prove that for any natural numbers a,b,ca , b , c that b>a>1b>a>1 and gcd(c,ab)=1gcd(c,ab)=1 , there exist a natural number nn such that : c∣(bnan)c | \binom{b^n}{a^n}
Proposed by Navid Safaei
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