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Kvant 2021
M2645
M2645
Part of
Kvant 2021
Problems
(1)
NT game with common multiples
Source: Kvant Magazine No. 3 2021 M2645
3/9/2023
Vitya wrote down
n
n{}
n
different natural numbers in his notebook. For each pair of numbers from the notebook, he wrote out their smallest common multiple on the board. Could it happen for some
n
>
100
n>100
n
>
100
that
n
(
n
ā
1
)
/
2
n(n-1)/2
n
(
n
ā
1
)
/2
numbers on the board are (in some order) consecutive terms of a non-constant arithmetic progression?Proposed by S. Berlov
number theory
Kvant