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April 20, 2014

April 20, 2014

Posted by **jamie** on Thursday, June 7, 2007 at 12:51pm.

remainder of 3 when divided by 4 and a remainder of 4 when divided by 5?

The answer is 59. There is a general method for solving such problms, but in this case you can use this trick. First, note that you don't have to demand that the remainder is 1 when divided by 2 becuse that follows from the fact that the remainder is 3 when divided by 4.

The number 60 is the product of 3, 4, and 5. All the remainders for 60 are thus zero and 60 is the smallest positive number with this property. Now, all the remainders of 60 + x are equal to x. But if x is equal or larger than y then the remainder after division by y is obtained by subtracting y until the number becomes less than y. In case x is negative you have to add y as many times to make the number equal or larger to zero.

If we take x equal to -1, then all the remainders are -1 plus the number you are dividing with, so it's one less than the number, which is exactly what we want.

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