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Perfect Square Sum - Not (Posted on 2015-07-08) Difficulty: 3 of 5
Without actual evaluation, prove that 2015 is not expressible as the sum of precisely three perfect squares.

No Solution Yet Submitted by K Sengupta    
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Solution Solution Comment 1 of 1

As 2015 is worth 7, mod 8, it cannot be expressible as the sum of 3 squares, each of which must be congruent to {0,1,4}, mod 8.

As 2015 is odd, one or all 3 squares must be odd:

Odd + odd + odd= 1+1+1 = 3 mod 8.

Odd + even + even  = 1+0+0, 1+0+4, 1+4+4, mod 8; or {1,5} mod 8.



  Posted by broll on 2015-07-08 12:04:49
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