X is a positive integer > 1 and, P is a prime number.
Determine all possible pairs (X, P) such that
P^{X} + 144 is a perfect square.
let p^x+144=k^2 then
p^x+12^2=k^2
p^x=k^212^2
p^x=(k+12)(k12)
now since p is prime then either
k+12=k12 which can't happen or
k12=1 thus k=13 and
p^x=13 thus p=13 and x=1
thus the only solution is (1,13)

Posted by Daniel
on 20100112 11:53:50 