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Math Help - Sum of Two integer square PROOF

  1. #1
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    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
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  2. #2
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    Hint:

    consider

    a^2 + b^2 = 4k + 3

    what does this tell you? What happens if  a,b are both odd, both even, one is odd one is even?
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  3. #3
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    Quote Originally Posted by gmatt View Post
    Hint:

    consider

    a^2 + b^2 = 4k + 3

    what does this tell you? What happens if  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
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  4. #4
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    Quote Originally Posted by AwesomeDesiKid View Post
    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 a=2s b=2t + 1, what then does a^2 +b^2 look like?
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