MathDB

All

n+3

offices of University of Somewhere are numbered with numbers

0,1,2, \ldots ,

n+1,

n+2

for some

n \in \mathbb{N}

. One day, Professor

D

came up with a polynomial with real coefficients and power

n

. Then, on the door of every office he wrote the value of that polynomial evaluated in the number assigned to that office. On the

i

th office, for

i

\in

\{0,1, \ldots, n+1 \}

he wrote

2^i

and on the

(n+2)

th office he wrote

2^{n+2}

-n-3

.
[*] Prove that Professor D made a calculation error [*] Assuming that Professor D made a calculation error, what is the smallest number of errors he made? Prove that in this case the errors are uniquely determined, find them and correct them.

Problem Statement