Solved - Maths enthuziasts
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16 Sep 2007, 19:05
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Just a cute one (i'm not really in the mood for long calculations)
Considering p and 8*(p^2)+1 are prime numbers, show that 8*(p^2)-1 is also a prime number.
Who's up to it? :P
Considering p and 8*(p^2)+1 are prime numbers, show that 8*(p^2)-1 is also a prime number.
Who's up to it? :P
ok got it :D
Let's take p = 3k-1 => 8pp+1 = 8*(9kk-18+1)+1 = 72kk-144k+9, can be divided again through 3, can't be prime either.
Thus p=3k, and the only prime number of this form is 3. 8pp+1=73, it's prime, so 8pp-1=71, a prime number.
No maths enthusiasts around :<