If #m^2+n^2=10p^2+10p+1#, where #m# and #n# are positive integers and #p# is a prime number, what is #m+n# in terms of #p#?

Question

The answer is #4p+3# but I'm not sure how to get there.

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Answer 1 · 2016-08-30T23:09:01

Check the numbers, please.

To attain the answer #m+n=4p+3# it will be necessary to have the following numbers.

#m^2+n^2=16p^2+24p+1#