12

Part of 2004 Iran MO (3rd Round)

Problems(1)

Source: Iran 2004

\mathbb{N}_{10}

is generalization of

\mathbb{N}

that every hypernumber in

\mathbb{N}_{10}

is something like:

\overline{...a_2a_1a_0}

a_i \in {0,1..9}

\overline {...000} \in \mathbb{N}_{10}

) Also we easily have

+,*

\mathbb{N}_{10}

k

a*b

k

nubmer of (first

k

number of a * first

k

number of b) first

k

a+b

k

nubmer of (first

k

number of a + first

k

number of b) Fore example

\overline {...999}+ \overline {...0001}= \overline {...000}

Prove that every monic polynomial in

\mathbb{N}_{10}[x]

d

d^2

algebrapolynomialalgorithmgeometrygeometric transformationinductionnumber theory