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>? | + | 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== | ||
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==See also== | ==See also== | ||
| − | {{USAJMO newbox|year=2017|num-b= | + | {{USAJMO newbox|year=2017|num-b=3|num-a=5}} |
of positive integers such that 
is prime that properly divides the positive number 
?
