A Quick and Easy Diophantine Equation | Primes

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[LogicQuest]

Thank you for this question. Gratitude.

[angelishify]

The restriction to prime numbers is a considerable simplification of this problem. It could also be stated in the title (prime integers).

[allanmarder]

Just for the record: An example of integer solutions where one of them is not prime (17, 12) 17^2 -2*(12^2) = 289- (2*144) =1.

[mystychief]

Without the restriction of primes, when allowed only whole numbers, the smaller solutions are (±1, 0) and (±3, ±2), so 2+4=6 of them. I see in the comments also (±17, ±12) as 4 solutions. Note that y is indeed even. There are probably more solutions.

[Blaqjaqshellaq]

Let's say that x and y have to be positive but don't have to be prime. Can you prove that (3, 2) is still the only solution? (Or can you find other solutions?)

[johns.]

Here's one that's a bit trickier: x^2 - 32y^2 = 1

[jejnsndn]

From where you get geometric problems?