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prove that if x and y are odd positive integers , then x2+y2 is even not divisible by 4
Asked by jeetbhalerao12 | 30 Aug, 2018, 07:16: PM
answered-by-expert Expert Answer
General form of odd number 2n+1
Let the two odd positive numbers be x = 2n + 1 and y = 2m + 1
Hence x2 + y2 = (2n + 1)2 + (2m + 1)2
                     = 4n2 + 4n + 1 + 4m2 + 4m + 1
                     = 4n2 + 4m2 + 4n + 4m + 2
                     = 4(m2 + n2 + m + n) + 2
Clearly notice that the sum of square is even the number is not divisible by 4
Hence if x and y are odd positive integers, then x2 + y2 is even but not divisible by 4
Answered by Arun | 31 Aug, 2018, 11:23: AM

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