On a theorem of Kanold on odd perfect numbers

A. S. Bang, Taltheoretiske Undersøgelser, Tidsskrift Math. 5 IV (1886), 70–80 and 130–137.

G. L. Cohen and R. J. Williams, Extensions of some results concerning odd perfect numbers, Fibonacci Quart. 23 (1985), 70–76.

L. E. Dickson, On the cyclotomic function, Am. Math. Monthly 12 (1905), 86–89.

S. Adam Fletcher, Pace P. Nielsen and Pascal Ochem, Sieve methods for odd perfect numbers, Math. Comp. 81 (2012), 1753–1776.

Peter Hagis Jr. and Wayne L. McDaniel, A new result concerning the structure of odd perfect numbers, Proc. Am. Math. Soc. 32 (1972), 13–15.

Hans-Joachim Kanold, Untersuchungen über ungerade vollkommene Zahlen, J. Reine Angew. Math. 183 (1941), 98–109.

Hans-Joachim Kanold, Sätze über Kreisteilungspolynome und ihre Anwendungen auf einige zahlentheoretische Probleme, I, J. Reine Angew. Math. 187 (1950), 169–182.

Hans-Joachim Kanold, Über ein spezielles System von zwei diophantischen Gleichungen, J. Reine Angew. Math. 189 (1950), 243–245.

Wayne L. McDaniel, The non-existence of odd perfect numbers of a certain form, Arch. Math. (Basel) 21 (1970), 52–53.

Wayne L. McDaniel and P. Hagis Jr., Some results concerning the non-existence of odd perfect numbers of the form $$p^{a}M^{2\beta }$$, Fibonacci Quart. 13 (1975), 25–28.

T. Nagell, Introduction to Number Theory, Second edition, Chelsea, New York, 1964.

Pace P. Nielsen, An upper bound for odd perfect numbers, Integers 3 (2003), #A14.

Pace P. Nielsen, Odd perfect numbers, diophantine equations, and upper bounds, Math. Comp. 84 (2015), 2549–2567.

R. Steuerwald, Verschärfung einer notwendigen Bedingung für die Existenz einen ungeraden vollkommenen Zahl, S.-B. Bayer. Akad. Wiss. 1937, 69–72.

Tomohiro Yamada, Odd perfect numbers of a special form, Colloq. Math. 103 (2005), 303–307.

Tomohiro Yamada, A new upper bound for odd perfect numbers of a special form, Colloq. Math. 156 (2019), 15–23, corrigendum, ibid. 162 (2020), 311–313.

Tomohiro Yamada, An exponential diophantine equation related to odd perfect numbers, Acta Math. Univ. Comenian. 90 (2021), 145–155.

K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. für Math. 3 (1892), 265–284.