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2 sequences with quotients and remainders

Source: Polish MO Recond Round 1981 p4

September 9, 2024

number theoryremainder

Problem Statement

The given natural numbers are

k, n

. We inductively define two sequences of numbers

(a_j)

and

(r_j)

as follows: Step one: we divide

k

by

n

and get the quotient

a_1

and the remainder

r_i

, step j: we divide

k+r_{j-1}

by

n

and get the quotient

a_j

and the remainder

r_j

. Calculate the sum of

a_1 + \ldots + a_n

.

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