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A 2006 Problem (Posted on 2006-07-27) Difficulty: 3 of 5
Determine the remainder when 612006 is divided by 2006.

Can you do this in a short time using pen and paper, and eventually a hand calculator, but no computer programs?

See The Solution Submitted by K Sengupta    
Rating: 3.3333 (3 votes)

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Advice (Read only if you are really stuck) | Comment 1 of 8
I scratched my head a lot and finally concluded that there is a straightforward way, somewhat lengthy, to solve this.  The fundamental principles of arithmetic mod 2006 will need to be exploited numerous times.  Note that 2006^2 is around 4 million and is therefore well within calculator range.  Reducing mod 2006 while performing a frequently-used algorithm for raising to a large power are the keys -- think binary.

BTW, the answer is 145.

  Posted by Richard on 2006-07-27 13:54:30
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