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Sum of lcm's

Source: 2024 Taiwan Mathematics Olympiad

January 31, 2024

number theoryTaiwanleast common multiple

Problem Statement

A positive integer is superb if it is the least common multiple of

1,2,\ldots, n

for some positive integer

n

. Find all superb

x,y,z

such that

x+y=z

.
Proposed by usjl