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2007 Guts #34: The Game

Source:

June 22, 2012
number theoryrelatively prime

Problem Statement

The Game. Eric and Greg are watching their new favorite TV show, The Price is Right. Bob Barker recently raised the intellectual level of his program, and he begins the latest installment with bidding on following question: How many Carmichael numbers are there less than 100,000100,000?
Each team is to list one nonnegative integer not greater than 100,000100,000. Let XX denote the answer to Bob’s question. The teams listing NN, a maximal bid (of those submitted) not greater than XX, will receive NN points, and all other teams will neither receive nor lose points. (A Carmichael number is an odd composite integer nn such that nn divides an−1−1a^{n-1}-1 for all integers aa relatively prime to nn with 1<a<n1<a<n.)
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