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September 23, 2014

September 23, 2014

Posted by **Joe** on Tuesday, September 16, 2008 at 10:15am.

- Math -
**Don**, Tuesday, September 16, 2008 at 11:16amthe smallest number I got was:

2519

- Math -
**David Q**, Tuesday, September 16, 2008 at 1:58pmI don't believe there's a smaller one than that (I checked it in Excel). The next one is 5039, which is twice the last plus 1. (Incidentally, the one before 2519 corresponds to N=-1.) To work out which number gives a remainder of 1 for all the integers from 1 to P, work out the least common multiple of all the numbers from 2 to P, and subtract 1. So for P=10, the LCM of 2, 3, 4, 5, 6, 7, 8, 9 and 10 is 2x3x2x5x7x2x3=2520; subtract 1 and you get your 2519.

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