x^2 + (x+1 )^2 =365 x^2 +x^2 + 2x +1 =365 2x^2 + 2x = 364 x^2 + x = 182 = (x- 13)(x + 14) x =13, so integers are 13 and 14, squares 169 and 196, which total 365.
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The consecutive integers whose sum is 51 are 16, 17, and 18.
99 = 9*11
The integers are 39 and 40.
The integers are 99, 100 and 101. There is also a set of consecutive even integers whose sum is 300. That set is 98, 100 and 102.
The integers are 16, 17 and 18.