Square number

**Mhmh96** · April 8th 2012, 05:05 AM

is equal square number ,what is the number?

**Sylvia104** · April 8th 2012, 05:24 AM

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

**Mhmh96** · April 8th 2012, 05:39 AM

(n+1)(n+1)?

**Soroban** · April 8th 2012, 07:14 AM

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:

$(123456)^2 + 123456 + 123457$

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

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

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

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

$\text{Answer: }\:123457$

**Mhmh96** · April 9th 2012, 07:46 AM

thanks for your help,and for correcting the question.

**Mhmh96** · April 9th 2012, 07:54 AM

Now i understand what is the hint

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