On equal values of power sums
B. Brindza ; Á. Pintér
Acta Arithmetica, Tome 76 (1996), p. 97-101 / Harvested from The Polish Digital Mathematics Library
Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:206910
@article{bwmeta1.element.bwnjournal-article-aav77i1p97bwm,
     author = {B. Brindza and \'A. Pint\'er},
     title = {On equal values of power sums},
     journal = {Acta Arithmetica},
     volume = {76},
     year = {1996},
     pages = {97-101},
     zbl = {0944.11009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav77i1p97bwm}
}
B. Brindza; Á. Pintér. On equal values of power sums. Acta Arithmetica, Tome 76 (1996) pp. 97-101. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav77i1p97bwm/

[000] [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).

[001] [2] B. Brindza, On S-integral solutions of the equations ym=f(x), Acta Math. Hungar. 44 (1984), 133-139.

[002] [3] B. Brindza, On some generalizations of the diophantine equation 1k+2k+...+xk=yz, Acta Arith. 44 (1984), 99-107. | Zbl 0497.10010

[003] [4] L. Carlitz, Note on irreducibility of the Bernoulli and Euler polynomials, Duke Math. J. 19 (1952), 475-481. | Zbl 0047.25401

[004] [5] J. W. S. Cassels, Integral points on certain elliptic curves, Proc. London Math. Soc. 14 (1965), 55-57. | Zbl 0134.27501

[005] [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. | Zbl 0121.28403

[006] [7] K. Dilcher, On a diophantine equation involving quadratic characters, Compositio Math. 57 (1986), 383-403. | Zbl 0584.10008

[007] [8] K. Győry, R. Tijdeman and M. Voorhoeve, On the equation 1k+2k+...+xk=yz, Acta Arith. 37 (1980), 234-240. | Zbl 0365.10014

[008] [9] H. Kano, On the equation s(1k+2k+...+xk)+r=byz, Tokyo J. Math. 13 (1990), 441-448. | Zbl 0722.11022

[009] [10] W. Ljunggren, Solution complète de quelques équations du sixième degré à deux indéterminées, Arch. Math. Naturv. (7) 48 (1946), 26-29. | Zbl 0060.09103

[010] [11] P. J. McCarthy, Irreducibility of certain Bernoulli polynomials, Amer. Math. Monthly 68 (1961), 352-353. | Zbl 0098.24803

[011] [12] H. Rademacher, Topics in Analytic Number Theory, Springer, Berlin, 1973.

[012] [13] J. J. Schäffer, The equation 1p+2p+...+np=mq, Acta Math. 95 (1956), 155-189. | Zbl 0071.03702

[013] [14] S. Uchiyama, Solution of a Diophantine problem, Tsukuba J. Math. 8 (1984), 131-137. | Zbl 0544.10011

[014] [15] J. Urbanowicz, On the equation f(1)1k+f(2)2k+...+f(x)xk+R(x)=byz, Acta Arith. 51 (1988), 349-368. | Zbl 0661.10026

[015] [16] J. Urbanowicz, On diophantine equations involving sums of powers with quadratic characters as coefficients, I, Compositio Math. 92 (1994), 249-271. | Zbl 0810.11017

[016] [17] M. Voorhoeve, K. Győry and R. Tijdeman, On the diophantine equation 1k+2k+...+xk+R(x)=yz, Acta Math. 143 (1979), 1-8. | Zbl 0426.10019