MathDB

Putnam 2019 B5

Source:

December 10, 2019

Problem Statement

Let

F_m

be the

m

'th Fibonacci number, defined by

F_1=F_2=1

and

F_m = F_{m-1}+F_{m-2}

for all

m \geq 3

. Let

p(x)

be the polynomial of degree 1008 such that

p(2n+1)=F_{2n+1}

for

n=0,1,2,\ldots,1008

. Find integers

j

and

k

such that

p(2019) = F_j - F_k

.

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