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        riddles >> medium >> sum of squares
        
(Message started by: Christine on Dec 25^th, 2012, 1:10pm)

Title: sum of squares
Post by Christine on Dec 25^th, 2012, 1:10pm

(72, 73, 74)

72 = 6^2 + 6^2
73 = 3^2 + 8^2
74 = 5^2 + 7^2

How to prove that we cannot find more than 3 consecutive integers expressible as a sum of two squares only?

Title: Re: sum of squares
Post by peoplepower on Dec 25^th, 2012, 3:05pm

Looking at the possible congruence classes mod 4 for the sum of two squares, we see that the class corresponding to -1 is not possible.

Title: Re: sum of squares
Post by atyq on Jan 30^th, 2013, 9:43am

Are you waiting for a mathematical proof?

Title: Re: sum of squares
Post by Christine on Jan 30^th, 2013, 10:12am

on 01/30/13 at 09:43:22, atyq wrote:

Are you waiting for a mathematical proof?

No. I managed to figure it out.