On the distribution of r-totatives of an integer
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Let r ≥ 1 be a fixed integer. For positive integers a and b, their greatest r^th power common divisor is denoted by (a, b)_r. A positive integer τ with (τ ,n)_r=1 will be called a r-totative of n. The distribution of r-totatives of n in [0, n) is studied in this paper. The results established here generalize those of Lehmer [5],McCarthy [6] and Erdos[3] proved for the totatives (1-totatives) of n. Some of the proofs given here are by methods different from that of the earlier authors.
Abstract
Let r ≥ 1 be a fixed integer. For positive integers a and b, their greatest r^th power common divisor is denoted by (a, b)_r. A positive integer τ with (τ ,n)_r=1 will be called a r-totative of n. The distribution of r-totatives of n in [0, n) is studied in this paper. The results established here generalize those of Lehmer [5],McCarthy [6] and Erdos[3] proved for the totatives (1-totatives) of n. Some of the proofs given here are by methods different from that of the earlier authors.
참고문헌 (7)
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