# The smallest positive integer

Number Theory Level 3

Find the smallest positive integer $$N$$ having the following properties:

I. When $$N$$ is divided by 3 the remainder is 1;
II. When $$N$$ is divided by 5 the remainder is 2;
III. When $$N$$ is divided by 7 the remainder is 3;
IV. When $$N$$ is divided by 9 the remainder is 4.

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