Question 974869: What is the smallest possible integer that's greater than 100, and leaves a remainder of 1, when divided by 3; a remainder of 2, when divided by 5; and a remainder of 3, when divided by 7?
Answer by CubeyThePenguin(3113)   (Show Source):
You can put this solution on YOUR website! x = 1 mod 3
x = 2 mod 5
First find the integers that satisfy the first two conditions. The first number that works is 7, the next is 22, and so on. Any number of the form 7 + 15n, where n is a positive integer, leaves a remainder of 1 when divided by 3 and a remainder of 2 when divided by 5.
7 + 15n > 100
15n > 93
n > 6.2 ----> n = 7
We will start looking from 7 + 15(7) = 112 and beyond. 112 is divisible by 7 and 15 leaves a remainder of 1 when divided by 7, so the number that satisfies all three conditions is:
112 + 15(3) = 157.
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