MathDB
2018 preRMO p30 integer P(x), P(1) = 4 and P(5) = 136, P(3) ?

Source:

August 8, 2019
polynomialalgebra

Problem Statement

Let P(x)P(x) = a0+a1x+a2x2++anxna_0+a_1x+a_2x^2+\cdots +a_nx^n be a polynomial in which aia_i is non-negative integer for each ii \in {0,1,2,3,....,n0,1,2,3,....,n} . If P(1)=4P(1) = 4 and P(5)=136P(5) = 136, what is the value of P(3)P(3)?