garnirativ8

2022-10-07

Every odd prime can be expressed as the difference of two squares in one and only one way.
​(a) Find this one way for the prime number 37
​(b) Find this one way for the prime number 41

Do you have a similar question?

Recalculate according to your conditions!

goffaerothMotw1

Expert

Step 1
a) ${x}^{2}-{y}^{2}=37$
$\left(x+y\right)\left(x-y\right)=37$
let $x+y=37$
$x-y=1$
Add both $2x=38$
$x=38/2$
$x=19$
hence $y=37-19=18$
Thus $37={19}^{2}-{18}^{2}$
Step 2
b) ${x}^{2}-{y}^{2}=41$
$\left(x+y\right)\left(x-y\right)=41$
let $x+y=41$
$x-y=1$
Add both $2x=42$
$x=42/2$
$x=21$
hence $y=41-21=20$
Thus $41={21}^{2}-{20}^{2}$

Still Have Questions?

Free Math Solver