Suppose we have an unknown number of objects. When counted in threes, 2 are left over, when counted in fives, 3 are left over, and when counted in sevens, 2 are left over. How many objects are there?

Actually, combining the equations only tells us that x = 23 mod 105. There are infinitely many such x, in particular 23, 128, 233, 338, …. The general term is 23 + 105n.

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