a "well-known" result in shannon's paper "A mathematical theory of communication"

In Shannon's 1948 paper "A Mathematical Theory of Communication", early on he derives the equation
N(t) = N(t-t1) + N(t-t2) + … + N(t-tn)

He then says "according to a well-known result in finite differences, N(t) is then asymptotic for large t to (X0)^t where (X0)^t is the largest real solution of the equation
X^(-t1) + X^(-t2)+…+X^(-tn) = 1 "
He does not cite a reference.
Intuitively,it seems to be true.but someone can help me in details? or tell me the reference at least. thx~(Wondering)
here is the paper:
Attachment 22281

It's probably this theorem.