Determine all possible values of a positive integer N ≥ 3, such that
^{N}C
_{2} – 1 is a
prime power.
Note:
^{N}C
_{2} represents N
choose 2.
(In reply to
re: No Subject by farcear)
I was thinking of (n2) and (n+1) which if neither is 1 and they produce a prime power must be each be powers of 3.
The actual factors [1] (.5n1)(n+1) or [2] (n2)(.5n+.5) can differ by any value.
This does not change much since exponents grow so fast that
2*p^x+3 = p^y
and
p^x = 2*p^y  3
Only have solutions if p=3 anyway (p cannot be 2 due to the +3 or 3)

Posted by Jer
on 20100426 15:42:02 