MathDB

The symbols

(a,b,\ldots,g)

and

[a,b,\ldots,g]

denote the greatest common divisor and least common multiple, respectively, of the positive integers

a,b,\ldots,g

. For example, (3,6,18)\equal{}3 and [6,15]\equal{}30. Prove that \frac{[a,b,c]^2}{[a,b][b,c][c,a]}\equal{}\frac{(a,b,c)^2}{(a,b)(b,c)(c,a)}.

Problem Statement