sqrt(17p+625)=x
17p+625=x^2
17p=x^2-625
17p=(x+25)(x-25)
Therefore, x+25 and x-25 are either 1 and 17p, or 17 and p.
Case 1:x+25=1, x-25=17p
x=-24, but x-25=-49 is not divisible by 17.
Case 2:x+25=17p, x-25=1
x=26 and x+25=51, so p=3.
Case 3:x+25=17, x-25=p
x=-8, but x-25=-33 is not prime.
Case 4:x+25=p, x-25=17
x=42, so p=67.
Therefore, the answers are 3 and 67.
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Posted by Math Man
on 2013-02-15 21:54:56 |
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