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|before=2|num-a=4}} | ||
Revision as of 21:33, 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 | ||
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1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
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