My Math Forum Reverse Modulo

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 July 30th, 2009, 11:26 PM #1 Newbie   Joined: Jul 2009 Posts: 1 Thanks: 0 Reverse Modulo Hi, I have a little question. Is there a quick way to evaluate the smallest number (x) that matches the following condition? x modulo a = e x modulo b = f a, b, e and f are given and I want to compute the smallest or if that is not possible any number (x) that matches that condition. Example: x modulo 5 = 4 x modulo 7 = 5 The smallest number that matches that condition is 19. Other values are 54, 89,... My current solution is working like this 4 5 -> (4 < 5) -> 4+5 9 5 -> (9 > 5) -> 5+7 9 12 -> (9 < 12) -> 9+5 14 12 -> (14 > 12) -> 12+7 14 19 -> (14 < 19) -> 14+5 19 19 -> (19 = 19) -> finished But that seems kind of slow.
 August 5th, 2009, 10:12 PM #2 Newbie   Joined: Jul 2009 Posts: 21 Thanks: 0 Re: Reverse Modulo The problem is you forgot to remove the = when there are over 3 separate numbers in it. Try dat. <3
 August 6th, 2009, 04:53 AM #3 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Reverse Modulo You need Sunzi's theorem (the "Chinese remainder theorem"). I can't tell (!) if that's what you're doing above. Personally, I use Code: chinese(Mod(4, 5), Mod(5, 7)) in Pari.

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