Question

three consecutive integers are such that when they are taken in increasing order and x 2 3 and 4 these add up to 74 wht r these
numbers
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Answer 1

Let the two odd positive numbers be x = 2k + 1 a nd y = 2p + 1 Hence x2 + y2 = (2k + 1)2 + (2p + 1)2 = 4k2 + 4k + 1 + 4p2 + 4p + 1 = 4k2 + 4p2 + 4k + 4p + 2 = 4(k2 + p2 + k + p) + 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 cross check let m= 3 and n=5 3^2+5^2=34 34 is not divisible by 4 hence prove