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Bundeswettbewerb Mathematik 1979 Problem 2.4

Source: Bundeswettbewerb Mathematik 1979 Round 2

September 23, 2022

SequenceLast digitinfinitely many solutionsnumber theory

Problem Statement

An infinite sequence

p_1, p_2, p_3, \ldots

of natural numbers in the decimal system has the following property: For every

i \in \mathbb{N}

the last digit of

p_{i+1}

is different from

9

, and by omitting this digit one obtains number

p_i

. Prove that this sequence contains infinitely many composite numbers.