3

Part of 2013 Dutch BxMO/EGMO TST

Problems(1)

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

Source: Dutch BxMO/EGMO TST 2013 p3

Find all triples

(x,n,p)

of positive integers

x

n

p

for which the following holds

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

number theoryprimeDiophantine equation