Given

**a^2+15226=c^2**,

How many solutions (a,c) are there such that both numbers are positive integers?

Please comment upon the unexpected result.

*<o:p> </o:p>*

*since 15226= 2****7613 and 7613** is a prime number - let's solve for a general case:

(c+a) *(c-a) =2*p , p an odd prime

Solving for a & c there are 2 possible integer factorizations :

** c+a =2p c-a=1** or

**c+a=p , c-a=2**

**In both sets of equation there are no integer solutions:**

**c+a and c-a must be of the same parity, i.e. both odd or both even.**

**see my "spoiler" post**

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*Edited on ***March 1, 2018, 4:15 am**