MathDB

There is a broken computer such that only three primitive data

c

1

and

-1

are reserved. Only allowed operation may take

u

and

v

and output

u \cdot v + v.

At the beginning,

u,v \in \{c, 1, -1\}.

After then, it can also take the value of the previous step (only one step back) besides

\{c, 1, -1\}

. Prove that for any polynomial

P_{n}(x) = a_0 \cdot x^n + a_1 \cdot x^{n-1} + \ldots + a_n

with integer coefficients, the value of

P_n(c)

can be computed using this computer after only finite operation.

Problem Statement