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Bundeswettbewerb Mathematik 1981 Problem 1.1

Source: Bundeswettbewerb Mathematik 1981 Round 1

September 22, 2022

Digitsnumber theorypowers

Problem Statement

Let

a

and

n

be positive integers and

s = a + a^2 + \cdots + a^n

. Prove that the last digit of

s

is

1

if and only if the last digits of

a

and

n

are both equal to

1

.

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