IMO 1969 LL POL56

Let a and b be two natural numbers that have an equal number

imolonglistmathematicsolympiad

IMO 1969 LL POL56

Origin: POL

Problem

Let a and b be two natural numbers that have an equal number n of digits in their decimal expansions. The first m digits (from left to right) of the numbers a and b are equal. Prove that if m > n/2, then a1/n −b1/n < 1 n.