Difference between revisions of "1983 IMO Problems/Problem 3"
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Let <math>a</math>, <math>b</math> and <math>c</math> be positive integers, no two of which have a common divisor greater than <math>1</math>. Show that <math>2abc - ab - bc- ca</math> is the largest integer which cannot be expressed in the form <math>xbc + yca + zab</math>, where <math>x</math>, <math>y</math> and <math>z</math> are non-negative integers. | Let <math>a</math>, <math>b</math> and <math>c</math> be positive integers, no two of which have a common divisor greater than <math>1</math>. Show that <math>2abc - ab - bc- ca</math> is the largest integer which cannot be expressed in the form <math>xbc + yca + zab</math>, where <math>x</math>, <math>y</math> and <math>z</math> are non-negative integers. | ||
| − | {{IMO box|year=1983| | + | {{IMO box|year=1983|num-b=2|num-a=4}} |
Revision as of 21:35, 31 January 2016
Let 
, 
and 
be positive integers, no two of which have a common divisor greater than 
. Show that 
is the largest integer which cannot be expressed in the form 
, where 
, 
and 
are non-negative integers.
| 1983 IMO (Problems) • Resources | ||
| Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
| All IMO Problems and Solutions | ||
