Math CentralQuandaries & Queries


Question from vivek, a student:

what is the remainder when 2050*2071*2095 is divided by 23 ?
this question needs to be done in as less time as possible.

Well, calculators aside, you can do some quick arithmetic as follows by using multiples of 23 like 230, 2300, etc.

2300-230 =2070 is clearly a multiple of 23 so what would the remainder be if we divided (2070-2050)*(2070-2071)*(2070-2095) = 20*(-1)*(-25) by 23 and how would this relate to your question? (You could simplify even further by looking at (-3)*(-1)*(-2) instead of 20*(-1)*(-25); why?). I think your answer should be 17.

What is really going on here is the idea behind modular arithmetic, hope this helps,


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