sqrt(17p+625)=x
17p+625=x^2
17p=x^2625
17p=(x+25)(x25)
Therefore, x+25 and x25 are either 1 and 17p, or 17 and p.
Case 1:x+25=1, x25=17p
x=24, but x25=49 is not divisible by 17.
Case 2:x+25=17p, x25=1
x=26 and x+25=51, so p=3.
Case 3:x+25=17, x25=p
x=8, but x25=33 is not prime.
Case 4:x+25=p, x25=17
x=42, so p=67.
Therefore, the answers are 3 and 67.

Posted by Math Man
on 20130215 21:54:56 