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2015 MMATHS Tiebreaker p3 - can first three digits of n\pi are .001 ?

Source:

October 8, 2023

number theoryMMATHSalgebra

Problem Statement

Is there a number

s

in the set

\{\pi,2\pi,3\pi,...,\}

such that the first three digits after the decimal point of

s

are

.001

? Fully justify your answer.