Prove there is no positive integer n such that 2ⁿ divided by n gives a remainder of 1.

list
   10   for N= 1 to 999999999
   18    P=modpow(2,N,N)
   20    if P<10 and p @ 2 = 1  then print N,P
   30   next
OK
run

n            2^n mod n
 25              7
 1727            7
 19147           5
 2228071         9
 3830879         7
 16888457        9
 33554425        7
 352978207       9
OK

Both 1 and 3 are missing from this list, which doesn't mean that they won't show up with higher n.

Posted by Charlie on 2013-03-14 00:10:02