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Least n such that 2^2000 divides a^n-1

Source: Romanian TST 2000

February 18, 2011
modular arithmeticnumber theory proposednumber theory

Problem Statement

Let a>1a>1 be an odd positive integer. Find the least positive integer nn such that 220002^{2000} is a divisor of anāˆ’1a^n-1.
Mircea Becheanu
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