Question

Prove that if x and y are positive integers, then x2

+ y

2

is even but not divisible by 4.

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Answer 1

Answer:

As x2+y2 is of the form 2k, this means that it is divisible by 2 and hence it is even. Now, any integer when divided by 4 will be written as 4q+r ( Using Euclid's division lemma). ... Hence, it is proved that if, x and y are odd positive integers, then x2+y2 is even but not divisible by 4.