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Current Events > Can you find prime numbers p and q such that p^2 - 32q^2 = 1 ?

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FLOUR
10/06/23 9:31:45 PM
#1:


Using only logic and algebra. No guess and check. There's only one prime solution pair. Bonus points if you can explain why.

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Trumble
10/06/23 9:33:06 PM
#2:


42.

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MrResetti
10/06/23 9:33:37 PM
#3:


Do your own homework
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BurmesePenguin
10/06/23 9:34:32 PM
#4:


I don't want to.

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Sigful User Logic
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Trumble
10/06/23 9:35:20 PM
#5:


MrResetti posted...
Do your own homework
Tag checks out.

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WalkingPlague
10/06/23 9:45:40 PM
#6:


The equation youve given, p^2 - 32q^2 = 1, is a special case of Pells equation. Pells equation has the general form of x^2 - Dy^2 = 1, where D is a non-square positive integer.

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FLOUR
10/09/23 5:58:05 PM
#7:


No takers?

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thronedfire2
10/09/23 6:01:48 PM
#8:


probably...not?

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DKBananaSlamma
10/09/23 6:04:04 PM
#9:


use wolfram alpha and cheat like a normal person, bro

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Neon >_>
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