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lcm, [a, b] =1000, [b, c] = 2000, [c, a] =2000

Source: 2015 Moldova JBMO TST p8

February 25, 2021
number theoryleast common multipleLCM

Problem Statement

Determine the number of all ordered triplets of positive integers (a,b,c)(a, b, c), which satisfy the equalities: [a,b]=1000,[b,c]=2000,[c,a]=2000.[a, b] =1000, [b, c] = 2000, [c, a] =2000.
([x, y]represents the least common multiple of positive integers x,y)
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