MathDB

12.4

Part of 2024 Bulgarian Winter Tournament

Problems(1)

np is good for infinitely many primes p

Source: Bulgarian Winter Tournament 2024 12.4

1/28/2024
Call a positive integer mm <spanclass=′latex−italic′>good</span><span class='latex-italic'>good</span> if there exist integers a,b,ca, b, c satisfying m=a3+2b3+4c3−6abcm=a^3+2b^3+4c^3-6abc. Show that there exists a positive integer n<2024n<2024, such that for infinitely many primes pp, the number npnp is <spanclass=′latex−italic′>good</span><span class='latex-italic'>good</span>.
number theory