2

Part of 2014 German National Olympiad

Problems(1)

Divisibility of a certain sequence

Source: Germany 2014-Problem 2

For a positive integer

n

y_n

be the number of

n

-digit positive integers containing only the digits

2,3,5, 7

and which do not have a

5

directly to the right of a

2.

r\geq 1

m\geq 2

are integers, prove that

y_{m-1}

y_{rm-1}.

combinatoricsnumber theoryDivisibilitySequenceformula