MathDB
Blocks in fractions

Source: St. Petersburg 2023 11.3

August 12, 2023
number theory

Problem Statement

The infinite periodic fractions ab\frac{a} {b} and cd\frac{c} {d} with (a,b)=(c,d)=1(a, b)=(c, d)=1 are such that every finite block of digits in the first fraction after the decimal point appears in the second fraction as well (again after the decimal point). Show that b=db=d.
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