Abstract
Let P(x)=p dx d+⋯+p 0∈ Z[x] be such that d⩾1,p d=1,p 0⩾2 and N={0,1,…,p 0−1} . We are proving in this note a new criterion for the pair {P(x), N} to be a canonical number system. This enables us to prove that if p 2,…,p d−1,∑ i=1 dp i⩾0 and p 0>2∑ i=1 d|p i|, then {P(x), N} is a canonical number system.
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