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Kvant 2019
M2543
M2543
Part of
Kvant 2019
Problems
(1)
GCD has no more than 14 digits
Source: Kvant Magazine No. 1 2019 M2543
3/20/2023
Let
a
a
a
and
b
b
b
be 2019-digit numbers. Exactly 12 digits of
a
a
a
are non-zero: the five leftmost and seven rightmost, and exactly 14 digits of
b
b
b
are non-zero: the five leftmost and nine rightmost. Prove that the largest common divisor of
a
a
a
and
b
b
b
has no more than 14 digits.Proposed by L. Samoilov
number theory
Digits