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How Many Dividing Pairs?

Calvin Lin Shared by Calvin Lin

For how many integer values of \(i\), \(1 \leq i \leq 1000 \), does there exist an integer \(j \), \( 1 \leq j \leq 1000 \), such that \( i \) is a divisor of \( 2^j - 1 \)?

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This Number Theory problem was shared by Calvin Lin.