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Some number-theoretic identities from group actions

Authors:

Balasubramanian Sury

Affiliation:

(1) Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile Mysore Road, Bangalore, 560059, India

Abstract:

We apply group actions to some natural situations like the natural ‘linear’ action of GL _r (Z _n) and some of its subgroups to derive number-theoretic identities like

$sumlimits_{t_1 in (Z_n )^ * , t_2 , cdots , t_r in Z_n } {GCD(n, t_1 - 1, t_2 , cdots , t_r )} = varphi (n)sigma _{r - 1} (n)$

Keywords:

Not-Burnside lemma Cauchy-Frobenius formula Linear action of GL _r(Z _n) Generalized totient function

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