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If w is an even integer, then w^2 - 1 is not a prime number.

my current working.

prove by contradiction

If w is a even integer then w^2 -1 is a prime number.

if w = 2x

then [itex]w^{2}[/itex] -1

= [itex]4x^{2}[/itex] -1

I am not sure where to go from here, maybe congruence relations:

n+1 = ([itex]4x^{2}[/itex])y

([itex]4x^{2}[/itex])y | n+1 therefore this is a contradiction.

is this correct.

thanks.