A note on primes p with σ ( p m ) = z n

Maohua Le

Colloquium Mathematicae (1991)

  • Volume: 62, Issue: 2, page 193-196
  • ISSN: 0010-1354

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Le, Maohua. "A note on primes p with $σ(p^m)=z^n$." Colloquium Mathematicae 62.2 (1991): 193-196. <http://eudml.org/doc/210108>.

@article{Le1991,
author = {Le, Maohua},
journal = {Colloquium Mathematicae},
keywords = {sum of divisors function; prime powers},
language = {eng},
number = {2},
pages = {193-196},
title = {A note on primes p with $σ(p^m)=z^n$},
url = {http://eudml.org/doc/210108},
volume = {62},
year = {1991},
}

TY - JOUR
AU - Le, Maohua
TI - A note on primes p with $σ(p^m)=z^n$
JO - Colloquium Mathematicae
PY - 1991
VL - 62
IS - 2
SP - 193
EP - 196
LA - eng
KW - sum of divisors function; prime powers
UR - http://eudml.org/doc/210108
ER -

References

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  1. [1] J. Chidambaraswawy and P. Krishnaiah, On primes p with σ ( p α ) = m 2 , Proc. Amer. Math. Soc. 101 (1987), 625-628. 
  2. [2] C. F. Gauss, Disquisitiones Arithmeticae, Fleischer, Leipzig 1801. 
  3. [3] K. Inkeri, On the diophantine equation a ( x n - 1 ) / ( x - 1 ) = y m , Acta Arith. 21 (1972), 299-311. Zbl0228.10017
  4. [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). Zbl0028.00901
  5. [5] E. Lucas, Théorie des fonctions numériques simplement périodiques, Amer. J. Math. 1 (1878), 289-321. 
  6. [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. [7] A. Rotkiewicz, Note on the diophantine equation 1 + x + x 2 + . . . + x n = y m , Elemente Math. 42 (1987), 76. Zbl0703.11016
  8. [8] A. Takaku, Prime numbers such that the sums of the divisors of their powers are perfect squares, Colloq. Math. 49 (1984), 117-121. Zbl0551.10004
  9. [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. Zbl0624.10004

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