Category: Number Theory
This article is aimed at entry level Math Olympiad (AMC and AIME in U.S. , SMO Junior in Singapore, RMO in India). We have complied some of the most useful results and tricks in elementary number theory that helps in problem solving at this level. Note that only with a lot of practice and conceptual…
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.
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…