1. ## Square number

is equal square number ,what is the number?

2. ## Re: Square number

Let $n=123456.$ Then the expression is $(n+1)+n+n^2=1+2n+n^2.$ Now factorize $1+2n+n^2.$

(n+1)(n+1)?

4. ## Re: Square number

Hello, Mhmh96

You may have missed the point of Sylvia's hint . . .

$123457 \;+\; 123456 \;+\; (123456)^2\text{ is the square of an integer.}\;\text{ What is the integer?}$

Look at what we have:

$(123456)^2 + 123456 + 123457$

. . $=\;(123456)^2 + 123456 + 123456 + 1$

. . $=\;(123456)^2 + 2(123456) + 1$

. . $=\;(123456 + 1)^2$

. . $=\;(123457)^2$

$\text{Answer: }\:123457$

5. ## Re: Square number

thanks for your help,and for correcting the question.

6. ## Re: Square number

Now i understand what is the hint