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2+22+222+...

Source: Moldova 2000 Grade 12 P3

April 27, 2021

algebra

Problem Statement

For any

n\in\mathbb N

, denote by

a_n

the sum

2+22+222+\cdots+22\ldots2

, where the last summand consists of

n

digits of

2

. Determine the greatest

n

for which

a_n

contains exactly

222

digits of

2

.

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