A number theory problem by U Z

Number Theory Level 1

$x^{2}$ - $2 y^{2}$ = 1

where x and y are prime numbers

then x+ y =

2 solutions

U Z
Sep 22, 2014

$x^{2}$ =2 $y^{2}$ +1 Therefore x is an odd number

Let x = $\boxed{2n +1}$

4 $n^{2}$ + 1 +4n = 2 $y^{2}$ +1

Therefore $y^{2}$ = 2 $n^{2}$ +2n Therefore y is an $\boxed{even prime number}$ Therefore y = $\boxed{2}$ and thus x = 3

i think it must be 17 and 12..

Ronabelle Camba - 6 years, 8 months ago

see y is a prime number and we get y as an even number and we know there is only 2 as a even prime number therefore y=2 and x=3

U Z - 6 years, 8 months ago

Dipak Bhais
Oct 7, 2014

we putting values of x=3 & y=2