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Iterated Specs (Posted on 2010-05-28) Difficulty: 2 of 5
There is a number N such that if you inscribe an N-gon in a circle, with all its angles an equal number of integral degrees, that N-gon will necessarily be a regular N-gon, with equal side lengths.

Also, if M is the number of possible divisors of N, including 1 and N itself, then the number M also meets the same criteria: If you inscribe an M-gon in a circle, with all its angles an equal number of integral degrees, that M-gon will necessarily be a regular M-gon, with equal side lengths.

What are N and M?

See The Solution Submitted by Charlie    
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  Subject Author Date
Aha!Steve Herman2010-05-28 16:15:33
Some ThoughtsMore answers? (SPOILER?)Steve Herman2010-05-28 16:06:03
Solutionanother approachDej Mar2010-05-28 13:26:20
number theory approachDaniel2010-05-28 12:26:47
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