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diophantine x^3 + 3x + 14 = 2 p^n , where p is prime

Source: Dutch BxMO/EGMO TST 2013 p3

August 24, 2019

number theoryprimeDiophantine equation

Problem Statement

Find all triples

(x,n,p)

of positive integers

x

and

n

and primes

p

for which the following holds

x^3 + 3x + 14 = 2 p^n