MathDB

Given a prime number

p>5

. It is known that the length of the smallest period of the fraction

1/p

is a multiple of three. This period (including possible leading zeros) was written on a strip of paper and cut into three equal-length parts

a

b

c

(they may also have leading zeros). What could be the sum of the three periodic fractions:

0.(a)

0.(b)

, and

0.(c)

?
Proposed by A. Khrabrov

Problem Statement