# Square number

• Apr 8th 2012, 05:05 AM
Mhmh96
Square number
http://store1.up-00.com/Mar12/3Zb90292.jpg is equal square number ,what is the number?
• Apr 8th 2012, 05:24 AM
Sylvia104
Re: Square number
Let $\displaystyle n=123456.$ Then the expression is $\displaystyle (n+1)+n+n^2=1+2n+n^2.$ Now factorize $\displaystyle 1+2n+n^2.$ (Smile)
• Apr 8th 2012, 05:39 AM
Mhmh96
Re: Square number
(n+1)(n+1)?
• Apr 8th 2012, 07:14 AM
Soroban
Re: Square number
Hello, Mhmh96

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

Quote:

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

Look at what we have:

$\displaystyle (123456)^2 + 123456 + 123457$

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

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

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

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

$\displaystyle \text{Answer: }\:123457$

• Apr 9th 2012, 07:46 AM
Mhmh96
Re: Square number
thanks for your help,and for correcting the question.
• Apr 9th 2012, 07:54 AM
Mhmh96
Re: Square number
Now i understand what is the hint