If x and y are odd pos. Integers then proofs x2 plus y2 is even but no

1.	If x and y are odd pos. Integers then proofs x2 plus y2 is even but not divisible by 4
Answer» Let x = 2p + 1 and y = 2q + 1{tex}\\therefore \\quad x ^ { 2 } + y ^ { 2 } = ( 2 p + 1 ) ^ { 2 } + ( 2 q + 1 ) ^ { 2 }{/tex}{tex}= 4 p ^ { 2 } + 4 p + 1 + 4 q ^ { 2 } + 4 q + 1{/tex}{tex}= 4 \\left( p ^ { 2 } + q ^ { 2 } + p + q \\right) + 2{/tex}{tex}= 2 \\left( 2 p ^ { 2 } + 2 q ^ { 2 } + 2 p + 2 q + 1 \\right){/tex}{tex}= 2 m \\quad \\text { where } m = \\left( 2 p ^ { 2 } + 2 q ^ { 2 } + 2 p + 2 q + 1 \\right){/tex}{tex}\\therefore \\quad x ^ { 2 } + y ^ { 2 }{/tex}\xa0is an even number but not divisible by 4.\xa0

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