query: Previous year Olympiad problem (polynomials)
positive_passages.docid: 143481
positive_passages.text: If $P(n)$ divides $P(P(n)-2015)$, prove that $P(-2015)=0$
negative_passages.docid: 68882
negative_passages.text: Path to Combinatorics Problem [$1.11$]
negative_passages.docid: 154487
negative_passages.text: Maximal number of monomials of multivariate polynomial
negative_passages.docid: 77864
negative_passages.text: Find $P(12)$ when $P(x)={1\over(x+1)}$, for $x=0,1,2,......11$
negative_passages.docid: 36207
negative_passages.text: I am unsure about this question using hermite polynomials and satifying recurrence relations
negative_passages.docid: 134570
negative_passages.text: Using Inclusion/Exclusion to solve $x_1+x_2+x_3=15$ with $x_1,x_2\leq 5$ and $x_3\leq 7$ for non negative integers $x_1,x_2,x_3$
negative_passages.docid: 135768
negative_passages.text: Find $P(n+1)$ for a polynomial P
negative_passages.docid: 58149
negative_passages.text: Working with symmetric polynomials
negative_passages.docid: 36362
negative_passages.text: What's wrong with my solution for the birthday problem?
negative_passages.docid: 76327
negative_passages.text: Finding inverse of polynomial in a field
negative_passages.docid: 54212
negative_passages.text: Another polynomial equation
negative_passages.docid: 118969
negative_passages.text: Olympiad Inequality $\sum\limits_{cyc} \frac{x^4}{8x^3+5y^3} \geqslant \frac{x+y+z}{13}$
negative_passages.docid: 106485
negative_passages.text: Olympiad Geometry Problem
negative_passages.docid: 14836
negative_passages.text: A polynomial sequence
negative_passages.docid: 110576
negative_passages.text: Let $P(x)$ be a polynolmial with degree $2009$ and leading coefficient unity such that $P(0)=2008,P(1)=2007,P(2)=2006,\ldots,P(2008)=0$,
negative_passages.docid: 139930
negative_passages.text: Find all polynomials $p$ such that $p(x^2)=p(x)p(x+1)$
negative_passages.docid: 43792
negative_passages.text: Find polynomials such that $(x-16)p(2x)=16(x-1)p(x)$