Question

Prove that every non-negative integer can be written as the sum of four squares.

          Prove that every non-negative integer can be written as the sum of four squares.
        

Added by Samantha P.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Prove that every non-negative integer can be written as the sum of four squares.
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Transcript

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00:01 Hi, now we are going to prove that sum of squares of three consecutive integers cannot be a square.
00:07 Let n -1, n and n plus 1 be the three consecutive integers.
00:23 Then sum of squares of three consecutive integers can be written as n -1 the whole squared plus n squared plus n plus 1 the whole squared and this will be equal to n squared minus 2n plus 1 plus n squared plus n squared plus 2n plus 1 and this will be equal to n squared plus n squared plus n squared plus 1 plus 1 and this can be written as 3n squared plus 2...
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