Before trying the problem "note your opinion as to whether the observed pattern is known to continue, known not to continue, or not known at all."

For integers greater than 1,
2ⁿ is never congruent to 1 (mod n)
2ⁿ is congruent to 2 (mod n) whenever n is prime, and sometimes when it isn't,
is 2ⁿ ever congruent to 3 (mod n)?

My first impression was that this was fairly obvious because of Fermat's little theorem. My instinct was that this guaranteed evenness.

Quite surprised to see a 3 in there.

A great series of problems, Jer.

Posted by broll on 2017-09-24 23:05:09