MathDB
Sums and products of digits and irrational numbers

Source: Macedonian TST for IMO 2013 - P2 day 1

March 28, 2021
number theoryirrational number

Problem Statement

a) Denote by S(n)S(n) the sum of digits of a positive integer nn. After the decimal point, we write one after the other the numbers S(1),S(2),...S(1),S(2),.... Show that the number obtained is irrational.
b) Denote by P(n)P(n) the product of digits of a positive integer nn. After the decimal point, we write one after the other the numbers P(1),P(2),...P(1),P(2),.... Show that the number obtained is irrational.
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