A note on primes p with $σ(p^m)=z^n$

• Autorzy: Maohua Le
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1991
• Tom: 62
• Numer: 2
• Strony: 193-196

Daty

wydano

1991

otrzymano

1990-03-14

Twórcy

autor

Maohua Le

• Research Department, Changsha Railway Institute, Changsha, Hunan, China

Bibliografia

• [1] J. Chidambaraswawy and P. Krishnaiah, On primes p with $σ(p^α)=m^2$, Proc. Amer. Math. Soc. 101 (1987), 625-628.
• [2] C. F. Gauss, Disquisitiones Arithmeticae, Fleischer, Leipzig 1801.
• [3] K. Inkeri, On the diophantine equation $a(x^n-1)/(x-1)=y^m$, Acta Arith. 21 (1972), 299-311.
• [4] W. Ljunggren, Some theorems on indeterminate equations of the form $(x^n-1)/(x-1)=y^q$, Norsk. Mat. Tidsskr. 25 (1943), 17-20 (in Norwegian).
• [5] E. Lucas, Théorie des fonctions numériques simplement périodiques, Amer. J. Math. 1 (1878), 289-321.
• [6] T. Nagell, Sur l'équation indéterminée $(x^n-1)/(x-1)=y^2$, Norsk Mat. Forenings Skr. (I) No. 3 (1921), 17 pp.
• [7] A. Rotkiewicz, Note on the diophantine equation $1+x+x^2+...+x^n=y^m$, Elemente Math. 42 (1987), 76.
• [8] A. Takaku, Prime numbers such that the sums of the divisors of their powers are perfect squares, Colloq. Math. 49 (1984), 117-121.
• [9] A. Takaku, Prime numbers such that the sums of the divisors of their powers are perfect power numbers, Colloq. Math. 52 (1987), 319-323.