Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Aug 31, 2012 #1
    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.
     
  2. jcsd
  3. Aug 31, 2012 #2
    Don't do it by contradiction, but use:

    w²-1=(w+1)(w-1)

    also there is the exception of w=2 since then (w+1)(w-1)=3 [itex]\cdot[/itex] 1=3 which is of course a prime. But by splitting it up this way we already see why. either side is the product of primes but this time one side is the empty product. But this is only true if w=2 since the integers as a ring have but one unit for multiplication.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: If w is an even integer, then w^2 - 1 is not a prime number.
  1. Probability w/ dice (Replies: 10)

Loading...