Difference between revisions of "2017 USAJMO Problems/Problem 4"

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==Problem==
 
==Problem==
Are there any triples <math>(a,b,c)</math> of positive integers such that <math>(a-2)(b-2)(c-2) + 12</math> is prime that properly divides the number <math>a^2 + b^2 + c^2 + abc - 2017</math>?
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Are there any triples <math>(a,b,c)</math> of positive integers such that <math>(a-2)(b-2)(c-2) + 12</math> is prime that properly divides the positive number <math>a^2 + b^2 + c^2 + abc - 2017</math>?
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==Solution 1==
  
==Solution==
 
  
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==See also==
 
==See also==
 
{{USAJMO newbox|year=2017|num-b=3|num-a=5}}
 
{{USAJMO newbox|year=2017|num-b=3|num-a=5}}

Revision as of 08:21, 18 January 2021

Problem

Are there any triples $(a,b,c)$ of positive integers such that $(a-2)(b-2)(c-2) + 12$ is prime that properly divides the positive number $a^2 + b^2 + c^2 + abc - 2017$?

Solution 1

See also

2017 USAJMO (ProblemsResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6
All USAJMO Problems and Solutions