My Math Forum appending a number to itself n times and finding modulo m

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 February 4th, 2017, 06:22 PM #1 Newbie   Joined: Feb 2017 From: DELHI Posts: 2 Thanks: 0 A number is given. That number is appended to itself n times (n can be as large as 10^10). I need to find the number thus formed modulo m. Let the number be 12 and n be 4, so number thus formed is 12121212. Let us find this number modulo 11, then the answer is 4. I tried to find the pattern like if the number is 12, I appended 12 again and took modulo with the given number (m) and went on appending and finding the modulo. For different m, I got different patterns. Sometimes it is alternate remainder and zero or sometimes 2*remainder kind of thing. But I could not find something concrete on which I can write an algorithm. Last edited by skipjack; February 6th, 2017 at 02:12 AM.
 February 6th, 2017, 03:01 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,476 Thanks: 2039 This thread is locked for a week as its author has pointed out that it is part of a problem in an open programming contest.

 Tags appending, finding, modular arithmetic, modulo, number, times

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# modulo of a number formed by appending number to itself

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