MathDB

Consider the polynomial P(x) \equal{} x^3 \plus{} 153x^2 \minus{} 111x \plus{} 38. (a) Prove that there are at least nine integers

a

in the interval

[1, 3^{2000}]

for which

P(a)

is divisible by

3^{2000}

. (b) Find the number of integers

a

[1, 3^{2000}]

with the property from (a).

Problem Statement