On equal values of power sums

B. Brindza; Á. Pintér

Acta Arithmetica (1996)

  • Volume: 77, Issue: 1, page 97-101
  • ISSN: 0065-1036

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B. Brindza, and Á. Pintér. "On equal values of power sums." Acta Arithmetica 77.1 (1996): 97-101. <http://eudml.org/doc/206910>.

@article{B1996,
author = {B. Brindza, Á. Pintér},
journal = {Acta Arithmetica},
keywords = {power sums; Bernoulli polynomials; exponential diophantine equations},
language = {eng},
number = {1},
pages = {97-101},
title = {On equal values of power sums},
url = {http://eudml.org/doc/206910},
volume = {77},
year = {1996},
}

TY - JOUR
AU - B. Brindza
AU - Á. Pintér
TI - On equal values of power sums
JO - Acta Arithmetica
PY - 1996
VL - 77
IS - 1
SP - 97
EP - 101
LA - eng
KW - power sums; Bernoulli polynomials; exponential diophantine equations
UR - http://eudml.org/doc/206910
ER -

References

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  1. [1] E. T. Avanesov, The Diophantine equation 3y(y+1) = x(x+1)(2x+1), Volž. Mat. Sb. Vyp. 8 (1971), 3-6 (in Russian). 
  2. [2] B. Brindza, On S-integral solutions of the equations y m = f ( x ) , Acta Math. Hungar. 44 (1984), 133-139. 
  3. [3] B. Brindza, On some generalizations of the diophantine equation 1 k + 2 k + . . . + x k = y z , Acta Arith. 44 (1984), 99-107. Zbl0497.10010
  4. [4] L. Carlitz, Note on irreducibility of the Bernoulli and Euler polynomials, Duke Math. J. 19 (1952), 475-481. Zbl0047.25401
  5. [5] J. W. S. Cassels, Integral points on certain elliptic curves, Proc. London Math. Soc. 14 (1965), 55-57. Zbl0134.27501
  6. [6] H. Davenport, D. J. Lewis and A. Schinzel, Equations of the form f(x) = g(y), Quart. J. Math. Oxford Ser. (2) 12 (1961), 304-312. Zbl0121.28403
  7. [7] K. Dilcher, On a diophantine equation involving quadratic characters, Compositio Math. 57 (1986), 383-403. Zbl0584.10008
  8. [8] K. Győry, R. Tijdeman and M. Voorhoeve, On the equation 1 k + 2 k + . . . + x k = y z , Acta Arith. 37 (1980), 234-240. Zbl0365.10014
  9. [9] H. Kano, On the equation s ( 1 k + 2 k + . . . + x k ) + r = b y z , Tokyo J. Math. 13 (1990), 441-448. Zbl0722.11022
  10. [10] W. Ljunggren, Solution complète de quelques équations du sixième degré à deux indéterminées, Arch. Math. Naturv. (7) 48 (1946), 26-29. Zbl0060.09103
  11. [11] P. J. McCarthy, Irreducibility of certain Bernoulli polynomials, Amer. Math. Monthly 68 (1961), 352-353. Zbl0098.24803
  12. [12] H. Rademacher, Topics in Analytic Number Theory, Springer, Berlin, 1973. 
  13. [13] J. J. Schäffer, The equation 1 p + 2 p + . . . + n p = m q , Acta Math. 95 (1956), 155-189. Zbl0071.03702
  14. [14] S. Uchiyama, Solution of a Diophantine problem, Tsukuba J. Math. 8 (1984), 131-137. Zbl0544.10011
  15. [15] J. Urbanowicz, On the equation f ( 1 ) 1 k + f ( 2 ) 2 k + . . . + f ( x ) x k + R ( x ) = b y z , Acta Arith. 51 (1988), 349-368. Zbl0661.10026
  16. [16] J. Urbanowicz, On diophantine equations involving sums of powers with quadratic characters as coefficients, I, Compositio Math. 92 (1994), 249-271. Zbl0810.11017
  17. [17] M. Voorhoeve, K. Győry and R. Tijdeman, On the diophantine equation 1 k + 2 k + . . . + x k + R ( x ) = y z , Acta Math. 143 (1979), 1-8. Zbl0426.10019

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