# Thread: Sum of Two integer square PROOF

1. ## Sum of Two integer square PROOF

Proove no integer of form 4K + 3 with k as an interger can we written as the sum of two suqares.
i kinda know but its hard to explain on paper
i need to know how to put this in to math

2. Hint:

consider

$\displaystyle a^2 + b^2 = 4k + 3$

what does this tell you? What happens if $\displaystyle a,b$ are both odd, both even, one is odd one is even?

3. Originally Posted by gmatt
Hint:

consider

$\displaystyle a^2 + b^2 = 4k + 3$

what does this tell you? What happens if $\displaystyle a,b$ are both odd, both even, one is odd one is even?
i knew that part, i knew that if a,b are even, then a^2 and b^2 would be even, then sum of them would be even, and if a,b were odd, then a^2 would be odd, and b^2 would be odd, but when u add 2 odd numbers, u would get something even

but i don't know about a case when u have a as odd and b as even, i mean i can't proove it by using math
p.s thanks for helping me soo many times

4. Originally Posted by AwesomeDesiKid
i knew that part, i knew that if a,b are even, then a^2 and b^2 would be even, then sum of them would be even, and if a,b were odd, then a^2 would be odd, and b^2 would be odd, but when u add 2 odd numbers, u would get something even

but i don't know about a case when u have a as odd and b as even, i mean i can't proove it by using math
p.s thanks for helping me soo many times
write $\displaystyle a=2s$ $\displaystyle b=2t + 1$, what then does $\displaystyle a^2 +b^2$ look like?