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Does it continue? 5: powers of 2 (Posted on 2017-09-24) Difficulty: 3 of 5
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)?

No Solution Yet Submitted by Jer    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Got me. | Comment 3 of 6 |

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
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