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m,n natural number, p prime: m(4m^2+m+12)=3(p^n-1)

Source: INMO 2013 P2

February 3, 2013
number theorygreatest common divisornumber theory proposed

Problem Statement

Find all m,n∈Nm,n\in\mathbb N and primes p≥5p\geq 5 satisfying m(4m2+m+12)=3(pn−1).m(4m^2+m+12)=3(p^n-1).
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