MathDB

6

Part of 2004 Polish MO Finals

Problems(1)

Successive terms of a sequence which are divisible by m

Source: Polish Mathematical Olympiad 2004 Final Round Problem 6

2/7/2010
An integer m>1 m > 1 is given. The infinite sequence (xn)n≥0 (x_n)_{n\ge 0} is defined by x_i\equal{}2^i for i<m i<m and x_i\equal{}x_{i\minus{}1}\plus{}x_{i\minus{}2}\plus{}\cdots \plus{}x_{i\minus{}m} for i≥m i\ge m. Find the greatest natural number k k such that there exist k k successive terms of this sequence which are divisible by m m.
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