How to solve the equation x*x-2=3y in integers?

Question

Mathematics

I tried on several numbers, it doesn't seem possible. But how to prove it? Thanks in advance.

Answer 1

Move the two to the right (x*x=3y+2) and calculate the left and right parts modulo 3 - analyze all possible cases (there are 3 of them)

Answer 2

x is divisible by 3: 9z² − 2 = 3y. The right is divisible by 3, the left is not.
Otherwise: (x−1)(x+1) = 3y + 1. At least one of the factors is a multiple of three. The opposite is true: the left is divisible by 3, the right is not.
Further, in my opinion, the proof cannot be simplified.

Answer 3

Based on the graph of the function , this is not possible.

Answer 4

prove through the change of sign when passing through the set of integers