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# Use Exercise 41 to determine whether M11 =211 ? 11 = 2047

ISBN: 9780073383095 37

## Solution for problem 43E Chapter 4.4

Discrete Mathematics and Its Applications | 7th Edition

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Problem 43E

Use Exercise 41 to determine whether M11 =211 ‒ 11 = 2047 and M17 =217 ‒ 1 = 131,071 are prime.

Let n be a positive integer and let n ‒ 1 = 2st,  where s is a nonnegative integer and 1 is an odd positive integer. We say that n passes Miller's test for the base b if either bt = 1 (mod n) or  (mod n) for some j with 0 ≤ j ≤ s ‒ 1. It can be shown (see [Rol0]) that a composite integer n passes Millers test for fewer than n/4 bases b with 1

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Use Exercise 41 to determine whether M11 =211 ? 11 = 2047

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