Prove that the sum of the squares of two consecutive odd integers leaves remainder 2 on division by 8

Question

Mathematics

Rylan Saunders

1 April, 11:01

Prove that the sum of the squares of two consecutive odd integers leaves remainder 2 on division by 8

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Tania · Answer 1

Two consecutive odd integers can be represented by 2x-1 and 2x+1 where x is any integer.

The sum of the squares is 4x²-4x+1+4x²+4x+1=8x²+2. If we divide by 8 we get x² and a remainder of 2.