MathDB

Let

f(x)=x^n + a_{n-1}x^{n-1} + ...+ a_0

be a polynomial of degree

n\ge 1

with

n

(not necessarily distinct) integer roots. Assume that there exist distinct primes

p_0,p_1,..,p_{n-1}

such that

a_i > 1

is a power of

p_i

, for all

i=0,1,..,n-1

. Find all possible values of

n

18