MathDB

Let

a

and

b

be 2019-digit numbers. Exactly 12 digits of

a

are non-zero: the five leftmost and seven rightmost, and exactly 14 digits of

b

are non-zero: the five leftmost and nine rightmost. Prove that the largest common divisor of

a

and

b

has no more than 14 digits.
Proposed by L. Samoilov

Problem Statement