Difference between revisions of "2019 OIM Problems/Problem 6"
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Let <math>a_1, a_2, \cdots , a_{2019}</math> be positive integers and <math>P</math> be a polynomial with integer coefficients such that, for every positive integer <math>n</math>, | Let <math>a_1, a_2, \cdots , a_{2019}</math> be positive integers and <math>P</math> be a polynomial with integer coefficients such that, for every positive integer <math>n</math>, | ||
| − | <cmath>P(n)|a_1^n+a_2^n+\cdots + a_{2019}^n</cmath> | + | <cmath>P(n)\;|\;a_1^n+a_2^n+\cdots + a_{2019}^n</cmath> |
Prove that <math>P</math> is a constant polynomial. | Prove that <math>P</math> is a constant polynomial. | ||
Latest revision as of 13:15, 14 December 2023
Problem
Let 
be positive integers and 
be a polynomial with integer coefficients such that, for every positive integer 
,
![\[P(n)\;|\;a_1^n+a_2^n+\cdots + a_{2019}^n\]](http://latex.artofproblemsolving.com/8/0/2/802ad7c3000d4a54a8c79fc42d20a54756a68d0e.png)
Prove that is a constant polynomial.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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