- #1
dgamma3
- 12
- 0
hello, I am trying to solve this problem:
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.
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.