\[\boxed{\text{662\ (662).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[Пусть\ x_{1},x_{2} -\]
\[последовательные\ \]
\[натуральные\ числа.\]
\[Составим\ уравнение:\]
\[{\left( x_{1} + x_{1} + 1 \right)^{2} = }{= x_{1}^{2} + \left( x_{1} + 1 \right)^{2} + 112}\]
\[\left( 2x_{1} + 1 \right)^{2} =\]
\[= x_{1}^{2} + x_{1}^{2} + 2x_{1} + 1 + 112\]
\[4x_{1}^{2} + 4x_{1} + 1 =\]
\[= 2x_{1}^{2} + 2x_{1} + 113\]
\[2x_{1}^{2} + 2x_{1} - 112 = 0\ \ \ \ \ |\ :2\]
\[x_{1}^{2} + x_{1} - 56 = 0\]
\[D = 1 + 224 = 225\]
\[x_{1,2} = \frac{- 1 \pm 15}{2} = 7;\ - 8 \notin N\]
\[то\ есть:\]
\[x_{1} = 7,\ x_{2} = 8.\ \]
\[Ответ:7\ и\ 8.\]