Difference between revisions of "1972 USAMO Problems/Problem 1"
(New page: ==Problem== The symbols <math>(a,b,\ldots,g)</math> and <math>[a,b,\ldots, g]</math> denote the greatest common divisor and least common multiple, respectively, of the positive integers <m...) |
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Revision as of 14:39, 30 December 2008
Problem
The symbols 
and ![$[a,b,\ldots, g]$](http://latex.artofproblemsolving.com/a/4/3/a435cfa873528fda8011ab1fee0f179f1233b4d5.png)
denote the greatest common divisor and least common multiple, respectively, of the positive integers 
. For example, 
and ![$[6,15]=30$](http://latex.artofproblemsolving.com/c/e/6/ce61f21da055164e6c4aa95b4ac1c682bb8075a7.png)
. Prove that
![$\frac{[a,b,c]^2}{[a,b][b,c][c,a]}=\frac{(a,b,c)^2}{(a,b)(b,c)(c,a)}$](http://latex.artofproblemsolving.com/a/3/7/a3797d87dfc7855e74fd6a01e4f48819256cecb4.png)
.Solution
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See also
| 1972 USAMO (Problems • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
