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2017 Iran TST2 day2 p6

Source: 2017 Iran TST second exam day2 p6

April 24, 2017

algebranumber theoryIranIranian TST

Problem Statement

Let

k>1

be an integer. The sequence

a_1,a_2, \cdots

is defined as:

a_1=1, a_2=k

and for all

n>1

we have:

a_{n+1}-(k+1)a_n+a_{n-1}=0

Find all positive integers

n

such that

a_n

is a power of

k

.
Proposed by Amirhossein Pooya

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