For every integer m such that 2 | m and 4 ∤ m, there exist no integers x and y for which x²+3y²= m. | Mathematics | Page 1

short ivyBOT May 27, 2024, 8:04 PM

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dawn dock May 27, 2024, 8:54 PM

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i got something using your path and the parity of numbers. I don't find a quicker way to solve it.

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||forall m in M , exists k in N sa, m = 2(2k+1)||

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if you want a small int

noble moon May 29, 2024, 9:56 AM

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OK. But is my quantifying statement correct?

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Or my assumption for proof by contradiction?

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@dawn dock

dawn dock May 29, 2024, 9:59 AM

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Both of them

#For every integer m such that 2 | m and 4 ∤ m, there exist no integers x and y for which x²+3y²= m.