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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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