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| Math Central | Quandaries & Queries |
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Question from vivek, a student: what is the remainder when 2050*2071*2095 is divided by 23 ? |
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,
Penny
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