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The explicit formula for the sequence

Source: Austrian Mathematical Olympiad 1997, Part 2, D1, P2

July 4, 2011
modular arithmeticnumber theory proposednumber theory

Problem Statement

A positive integer KK is given. Define the sequence (an)(a_n) by a1=1a_1 = 1 and ana_n is the nn-th positive integer greater than an−1a_{n-1} which is congruent to nn modulo KK.
(a) Find an explicit formula for ana_n.
(b) What is the result if K=2K = 2?
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