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Let P (x) = x d + p d−1 x d−1 + · · · + p 0 be an expanding monic polynomial with integer coefficients. If each element of Z[x]/P (x)Z[x] has a polynomial representative with coefficients in [0, |p 0 | − 1] then P (x) is called a canonical number system generating polynomial, or a CNS polynomial in short. A method due to Hollander  is employed to study CNS polynomials. Several new criteria for canonical number system generating polynomials are given and a conjecture of S.Akiyama & A.Pethődoi:10.4064/aa111-1-2 fatcat:texzb43r7naxzgbozg3dn3mdbe