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

Ponzi scheme (Bernie Madoff) o Taking new client money and giving it to old investors New investors stop coming in with new money o Seems legitimate Bernie had a 10%-12% return which is great but not outrageous o Comes from a well-respected and trusted individual Bernie was on wall street for years o All Ponzi...