# 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 | + | 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 |

## Revision as of 22:31, 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