Notes to the Feit-Thompson conjecture. II. (English) Zbl 1229.11004

Motose, Kaoru

Proc. Japan Acad., Ser. A 86, No. 8, 131-132 (2010).

Feit and Thompson conjectured for distinct primes \(p < q\) that \(\frac{q^{p}-1}{q-1}\) never divides \(\frac{p^{q}-1}{p-1}\). The author proves this for \(p=3\) and \(q\not\equiv -1\pmod 9\); \(p=5\) and \(q=5l-1\) with \(5 \nmid l\).
For Part I, see Proc. Japan Acad., Ser. A 85, No. 2, 16–17 (2009; Zbl 1228.11005).

Reviewer: Florin Nicolae (Berlin)

MSC:

11A07

Congruences; primitive roots; residue systems

Keywords:

Feit-Thompson conjecture

Citations:

Zbl 1228.11005

References:

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