Find the smallest positive integer n such that 2n −1 is divisible by 47.

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- Dec 7th 2007, 09:26 AManncarintegers and divisibility
Find the smallest positive integer n such that 2n −1 is divisible by 47.

- Dec 7th 2007, 09:40 AMSoroban
Hello, anncar!

Quote:

Find the smallest positive integer such that is divisible by 47.

If is divisible by 47, then: . for some integer

. . Then we have: .

Since is a positive integer, is divisible by 2.

. . The least value occurs when

Therefore: .