What is this calculation used for?
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I think one time I saw that in a Olympiad that they asked the question directly like: prove that all the primes of the form a^2 + b^2 = 4k+1 for some k. (Basically know the theorem or be a genius) Other than that I think I have never used it.
I can imagine a question like: Prove that if a^2 + b^2 is a prime then a^2 + b^2 -1 is a multiple of 4.
For the solution you substitute a^2 +b^2 with 4k +1 by the theorem and then 4k +1 -1 = 4k which is a multiple of 4.
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N6: Fermats last theorem
For n>2 there exists no a,b and c such that a^n + b^n = c^n
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Best theory:
1+1=2
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I can prove that 1+1 = 0
take a = b = 1 multiply by a on one side and by b on the other
a^2 = b^2 now subtract b^2 to one side and a^2 on the other (since a =b equality maintains)
a^2 - b^2 = b^2 - a^2 now we factorize
(a-b)(a+b) = b^2 - a^2 we know that b^2 - a ^2 = 0 since they are the same so:
(a-b)(a+b) = 0 then we divide by a-b
a+b = 0 since a and b are 1
1+1 = 0
therefore completing the proof
I will leave this as todays funny fact.
(DISCLAIMER: of course this is not true, there is a conceptual mistake in the proof that I won’t reveal yet to keep it magical)
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Where the fuck is the last part =1 of the a=b=1
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At the beginning I said a = 1 and b=1, I just saved this for the end
so because of this I can replace a and b with 1.
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Nerd thread.
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How is this possible?
I forgot completely about this thread lmao.
it’s because since I said a = b that means a-b = 0
And in the middle of that whole mess I divided by a-b AKA 0, and dividing by 0 is a mathematical sin. When someone showed me this for the first time I was amazed.
(funny thing, if you allow division by 0 you get that all numbers are equal to all other numbers, therefore 1+1=0 that is why it is undefined)
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Wait, I was always told dividing by zero does not work and is a bad idea. Man, Public School sucked.
It does not work ;-; sorry if I gave the idea it does MB.
What I am saying is that IF it was allowed (IT IS NOT) then weird things start happening and you can prove that all numbers equal all numbers which should NOT be (Therefore the reason why you CAN’T divide by 0).
Recap:
You CAN’T divide by 0 EVER!
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