Question

Suppose, we have a system of voting via the internet:
A1*a1+A2*a2+...+Ak*ak=T.
Here ai is a unique code of candidate, k is the number of candidates, Ai is the number of people, who voted for candidate with code ai, T is the sum of codes multiplied by number of voters, N=A1+A2+...+Ak is the number of voters.
How to choose parameters a1,a2... that, by knowing N, T and a1,a2,...ak we could easily find A1,A2,...,Ak? Suppose, we have a system of voting via the internet:
A1*a1+A2*a2+...+Ak*ak=T.
Here ai is a unique code of candidate, k is the number of candidates, Ai is the number of people, who voted for candidate with code ai, T is the sum of codes multiplied by number of voters, N=A1+A2+...+Ak is the number of voters.
How to choose parameters a1,a2... that, by knowing N, T and a1,a2,...ak we could easily find A1,A2,...,Ak? @Mathematics

Answer 1

e.g., when k=2, a1 could be 0 and a2=1. then T=A2 and N-T=A1