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IberoAmerican
2020 IberoAmerican
4
4
Part of
2020 IberoAmerican
Problems
(1)
Many gcd's and lcm's
Source: 2020 Iberoamerican #4
11/17/2020
Show that there exists a set
C
\mathcal{C}
C
of
2020
2020
2020
distinct, positive integers that satisfies simultaneously the following properties:
∙
\bullet
∙
When one computes the greatest common divisor of each pair of elements of
C
\mathcal{C}
C
, one gets a list of numbers that are all distinct.
∙
\bullet
∙
When one computes the least common multiple of each pair of elements of
C
\mathcal{C}
C
, one gets a list of numbers that are all distinct.
number theory