MathDB

Prove that for each natural number

d

, There is a monic and unique polynomial of degree

d

P

such that

P(1)

≠

0

and for each sequence like

a_{1}

a_{2}

...

of real numbers that the recurrence relation below is true for them, there is a natural number

k

such that

0=a_{k}=a_{k+1}= ...

P(n)a_{1} + P(n-1)a_{2} + ... + P(1)a_{n}=0

n>1

Problem Statement