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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
4 months, 4 weeks ago

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