# Thread: Square numbers

1. ## Square numbers

Could someone give me a method to this question?:

Rewrite 9991 as the difference of two squares. Use your answer to find the prime factors of 9991.

Than could someone give me methods to work out any of these annoying square number questions?

2. Originally Posted by Mukilab
Could someone give me a method to this question?:

Rewrite 9991 as the difference of two squares. Use your answer to find the prime factors of 9991.

Than could someone give me methods to work out any of these annoying square number questions?
As the last digit is a 1 I'm guessing 9 (3^2) is involved). Adding 9 to 9991 gives 10,000 which is also a square number

$\displaystyle 9991 = 10,000-9$

$\displaystyle 10000=100^2$
$\displaystyle 9 = 3^2$

Rewrite as the difference of two squares

3. Originally Posted by e^(i*pi)
As the last digit is a 1 I'm guessing 9 (3^2) is involved). Adding 9 to 9991 gives 10,000 which is also a square number

$\displaystyle 9991 = 10,000-9$

$\displaystyle 10000=100^2$
$\displaystyle 9 = 3^2$

Rewrite as the difference of two squares

thanks.

Really cleared a lot up

4. anothe method :
let $\displaystyle a^2-b^2=9991$, then $\displaystyle (a-b)(a+b)=9991$.
one of the solution (i think it is a trivial solution) is $\displaystyle a-b = 1$ and $\displaystyle a+b=9991$.
solve it, we get $\displaystyle a=4996$, and $\displaystyle b=4995$

5. Truly a fun method!

Thanks for the help