Difference between revisions of "2008 OIM Problems/Problem 3"
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== Problem == | == Problem == | ||
Let <math>m</math> and <math>n</math> be integers such that the polynomial <math>P(x) = x^3 + mx + n</math> has the following | Let <math>m</math> and <math>n</math> be integers such that the polynomial <math>P(x) = x^3 + mx + n</math> has the following | ||
| − | property: if <math>x</math> and <math>y</math> are integers and 107 divides <math>P(x) | + | property: if <math>x</math> and <math>y</math> are integers and 107 divides <math>P(x)-P(y)</math>, then 107 divides <math>x-y</math>. Show that 107 divides <math>m</math>. |
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
Latest revision as of 15:31, 14 December 2023
Problem
Let 
and 
be integers such that the polynomial 
has the following
property: if 
and 
are integers and 107 divides 
, then 107 divides 
. Show that 107 divides .
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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