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Divisibility Rules

Given a number $x$, can you determine if it is divisible by a number say $y$ with out even performing the actual division. Divisibility rules are quite handy when you want to test for divisibility of numbers even before you can actual divide the number. For instance, to check if a number is divisible by 7, […]

Using Chinese Remainder Theorem

A bag has certain number of pens. If you take out 3 pens at a time, 2 pens are left, if you take 4 pens, 1 pen is left and if you take 5 pens at a time, 3 pens are left in the bag. What is the smallest number of pens in the bag? […]