Difference between revisions of "1983 IMO Problems/Problem 4"
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==Problem== | ==Problem== | ||
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. | ||
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==Solution== | ==Solution== | ||
Revision as of 16:17, 22 August 2017
Problem
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.
