X is a positive integer > 1 and, P is a prime number.
Determine all possible pairs (X, P) such that
PX + 144 is a perfect square.
If X were given as 2, we would have the equation P2
, where P is the prime number and n is the root of the resulting perfect square. The equation is very much like that for a Pythagorean triple (a,b,c) where a2
There are four Pythagorean triples that fits Euclid's formula
[a = m2
: b = 2mn : c = m2
] with 12 as a side:
(5,12,13), which corresponds with 52
(9,12,20), which corresponds with 92
(12,16,20), which corresponds with 162
:: (8,2); and
(12,35,37)... but, as 35 is neither prime nor a perfect square, it is not a solution and does not lead to a solution.
Thus, no other solutions exist for X as 2 or as a multiple of 2.
Posted by Dej Mar
on 2010-01-12 14:41:51