Question

Find the number of ordered pairs x, y are prime numbers.

Answer 1

Infinite.................

Answer 2

hi friend!!
Here is another solution.
Rearranging the equation we get
x2−1=2y2x2−1=2y2
(x−1)(x+1)=2y2(x−1)(x+1)=2y2
Since yy is a prime number, 2y22y2 can only be the product of 1 and 2y22y2, or 2 and y2y2, or yy and 2y2y. Hence(Noticing that yy is not less than 2)

1.
x−1=1x−1=1
x+1=2y2x+1=2y2
Solution: yy is not an integer.

2.
x−1=2x−1=2
x+1=y2x+1=y2
Solution: x=3,y=2x=3,y=2

3.
x−1=yx−1=y
x+1=2yx+1=2y
Solution: x=3,y=2x=3,y=2

Answer: x=3,y=2
hope my answer helps you
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