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For a in Z, there are ∞ primes p s.t. p | n^2+3 & p | m^3-a

Source: Czech-Polish-Slovak Match, 2011

August 9, 2011
number theoryprime numbersrelatively primenumber theory unsolved

Problem Statement

Let aa be any integer. Prove that there are infinitely many primes pp such that p ∣ n2+3andp ∣ m3−a p\,|\,n^2+3\qquad\text{and}\qquad p\,|\,m^3-a for some integers nn and mm.
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