Školjka

%V0 $p=2x^2 - 1$ $p^2 = 2y^2 - 1$ $p | 2x^2 - 1 - 2y^2 + 1$ $p | 2(x-y)(x+y)$ $p=2$ nije rjesenje $p | (x-y)(x+y)$ $x = \sqrt{\frac{p+1}{2}} < p$ $y = \sqrt{\frac{p^2 + 1}{2}} < p$ $p|x-x \Rightarrow x=y \Rightarrow$ nema rjesenja $p|x+y \Rightarrow p=x+y$ $p+1=2x^2$ $p^2+1=2(p-x)^2$ $p^2+1=2p^2-4px+2x^2$ $1=p^2-4px+p+1$ $4x=p+1$ $p+1=\frac{p^2+2p+1}{8}$ $p^2-6p-7=0$ $(p-7)(p+1)=0$ $p=7$ je rjesenje