Digital Object Identifier (DOI)
This paper contains an elementary derivation of formulas for multiplicative functions of m which exactly yield the following numbers: the number of distinct arithmetic progressions of w reduced residues modulo m; the number of the same with first term n; the number of the same with mean n; the number of the same with common difference n. With m and odd w fixed, the values of the first two of the last three functions are fixed and equal for all n relatively prime to m; other similar relations exist among these three functions.
This work is licensed under a Creative Commons Attribution 3.0 License.
Was this content written or created while at USF?
Citation / Publisher Attribution
International Journal of Mathematics and Mathematical Sciences, v. 26, art. 340571
Scholar Commons Citation
Tanner III, Paul A., "Arithmetic Progressions that Consist only of Reduced Residues" (2001). Mathematics and Statistics Faculty Publications. 59.