- #1

nomadreid

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- Homework Statement
- N is the smallest positive integer such that N mod m = 1 for m in {2,3,4,5,6} and N mod 7 = 0. Find N.

- Relevant Equations
- This is supposed to be done without number theory theorems, and without a computer program, and of course not trial-and-error.

First, I know the answer: 301. I thought (despite the injunction that the problem is to be done without number theory) that the Chinese Remainder Theorem might be of help (if I would use a subset which contained only relatively primes), but that didn't get very far. I also tried to spot a pattern in a trial-and-error program (again, despite the injunction), but failed there. I thought it might be a combinatorial method, but that also did not yield any results. The solution is supposed to be relatively simple, so I am missing something obvious. (A bit embarrassing, as it is a problem for a 12-year old private student.)