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# Number Theory?

The numbers $$a_1, a_2, a_3, \ldots , a_{73}$$ are positive integers such that $$a_1 < a_2 < a_3 < \cdots < a_{73}$$.

Supose that the following condition is verified:
If $$i$$ and $$j$$ are integers between 1 and 73 such that $$i - j > 1$$ , then $$\frac { a_i - a_j }{ i - j }$$ is not an integer.
Determine the smallest value $$a_{73}$$ can take.

Note by John Smith
6 months, 3 weeks ago