Determine all primes m for which the quotient (2^m-1 - 1)/m is a perfect square.

(2^(3-1)-1)/3 = 1
(2^(7-1)-1)/7 = 9

with no other solutions through m=8563, where overflow took place in:

10 while m<1000000
20  m=nxtprm(m)
30  n=(2^(m-1)-1)/m
40  if n=int(n) then
50    :s=int(sqrt(n))
60    :if s*s=n then ? m,n
70 wend

Posted by Charlie on 2006-09-23 16:05:01