Problem - 03 - National Math Camp 2021 Number Theory Exam - "Infinitely many prime divisors"

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Anindya Biswas
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Problem - 03 - National Math Camp 2021 Number Theory Exam - "Infinitely many prime divisors"

Unread post by Anindya Biswas » Thu May 06, 2021 4:32 pm

Let $P(x)$ be a nonzero integer polynomial, that is, the coefficients are all integers. We call a prime $q$ "interesting" if there exists some natural number $n$ for which $q|2^n+P(n)$. Prove that there exist infinitely many “interesting” primes.
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
John von Neumann

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