Author: Ashani Dasgupta
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Arithmetic of Remainders
Consider the two number: 37 and 52 What is the remainder when we divide 37 by 7? 2 of course. And 52 produces remainder 3 when divided by 7. Suppose we want to know the remainder when the product of 37 and 52 is divided by 7.
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The Dreams of Pythagoras
Pythagoras is famous. Even those who do not like mathematics, have heard of Pythagoras’ Theorem (regarding right angled triangles). He lived about 2500 years ago and did about 2500 wonderful things (well may be a little less) but all that is not the subject matter of this note. We want to talk about the shattered…
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Chinese Remainder Theorem
I want to discuss the ‘ideai behind the famous Chinese Remainder Theorem. Let us leave the jargon and start our exploration by a problem.Find a number that leaves remainder 1, when divided by 5, 7 and 13. Clearly such a number can be found by trial. A stupid method is to check out all the…