SOLUTION: The positive integers p,q & r are all prime no.s if p^2-q^2=r,then find all posible values of r?

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Question 432963: The positive integers p,q & r are all prime no.s if p^2-q^2=r,then find all posible values of r?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
p%5E2+-+q%5E2+=+r, where p,q, and r are all prime.
p%5E2+-+q%5E2+=+%28p-q%29%28p%2Bq%29+=++r
Now p and q cannot both be odd primes at the same time, because by then p-q and p+q will both be even, and their product will be even, not prime. (Neither can we assume that p = q = 2. why?)
Hence we can assume that q is equal to 2 (the only even prime), whence
%28p-2%29%28p+%2B+2%29+=+r
==> p - 2 = 1 and p + 2 = r ==> p = 3 and r = 5.
OR
==> p - 2 = r and p + 2 = 1 ==> p = -1, which is not acceptable.
Thus, the only possible value of r is 5.