Neocijenjeno
7. svibnja 2019. 20:49 (1 tjedan, 6 dana)
Let A be a non-empty set of positive integers. Suppose that there are positive integers b_1,\ldots b_n and c_1,\ldots,c_n such that

- for each i the set b_iA+c_i=\left\{b_ia+c_i\colon a\in A\right\} is a subset of A, and

- the sets b_iA+c_i and b_jA+c_j are disjoint whenever i\ne j

Prove that {1\over b_1}+\,\ldots\,+{1\over b_n}\leq1.
Upozorenje: Ovaj zadatak još niste riješili!
Kliknite ovdje kako biste prikazali rješenje.