Hello, Mhmh96
You may have missed the point of Sylvia's hint . . .
$\displaystyle 123457 \;+\; 123456 \;+\; (123456)^2\text{ is the square of an integer.}\;\text{ What is the integer?}$
Look at what we have:
$\displaystyle (123456)^2 + 123456 + 123457$
. . $\displaystyle =\;(123456)^2 + 123456 + 123456 + 1$
. . $\displaystyle =\;(123456)^2 + 2(123456) + 1$
. . $\displaystyle =\;(123456 + 1)^2$
. . $\displaystyle =\;(123457)^2$
$\displaystyle \text{Answer: }\:123457$