Prove that if xand y are both add odd positive integer then x² +у is even but not divisible by 4
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Answer:We know that any odd positive integer is of the form 2q+1, where q is an integer.
Answer:We know that any odd positive integer is of the form 2q+1, where q is an integer. So, let x=2m+1 and y=2n+1, for some integers m and n.
Answer:We know that any odd positive integer is of the form 2q+1, where q is an integer. So, let x=2m+1 and y=2n+1, for some integers m and n. when have x²+y²
x²+y²=(2m+1)²+(2n+1)²
x²+y²=4m²+1+4m+4n²+1+4n
=4m²+4n²+4m+4n+2
x²+y²=4q+2…when q= (m²+n²) + m+n
x²+y² is even and leave remainder 2
when divided by 4
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