perplexus.info :: Just Math : Primed to Square

Primed to Square (Posted on 2013-02-15)

What is the largest prime p that makes sqrt(17p+625) an integer?

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 4.0000 (2 votes)

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| Comment 2 of 3 |

17p+625 = k^2

17p = (k+25)(k-25) and 17 factors at least one of the factors.

If (k+25) = 17a, p=a(17a-50). a=1 makes (17a-50) negative so (17a-50)=1 and a=p=3.

If (k-25) = 17a, p=a(17a+50). Here, (17a+50)=1 isn't possible so a=1, 17a+50=p=67.

Posted by xdog on 2013-02-15 20:12:31

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