MathDB

19

Part of 1983 IMO Shortlist

Problems(1)

Polynomial of degree 990

Source:

9/9/2010
Let (Fn)n≥1(F_n)_{n\geq 1} be the Fibonacci sequence F1=F2=1,Fn+2=Fn+1+Fn(n≥1),F_1 = F_2 = 1, F_{n+2} = F_{n+1} + F_n (n \geq 1), and P(x)P(x) the polynomial of degree 990990 satisfying P(k)=Fk, for k=992,...,1982. P(k) = F_k, \qquad \text{ for } k = 992, . . . , 1982. Prove that P(1983)=F1983−1.P(1983) = F_{1983} - 1.
algebrapolynomialFibonacciFibonacci sequenceSequenceIMO Shortlist