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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

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

It's probably this theorem.