A note on Jeśmanowicz' conjecture

• Autorzy: Maohua Le
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1996
• Tom: 69
• Numer: 1
• Strony: 47-51

Daty

wydano

1996

otrzymano

1994-06-20

Twórcy

autor

Maohua Le

• Department of Mathematics, Zhanjiang Teachers' College, P.O. Box 524048, Zhanjiang, Guangdong P.R. China

Bibliografia

• [1] R. Apéry, Sur une équation diophantienne, C. R. Acad. Sci. Paris Sér. I Math. 251 (1960), 1451-1452.
• [2] J.-R. Chen, On Jeśmanowicz' conjecture, J. Sichuan Univ. Nat. Sci. 1962 (2), 19-25 (in Chinese).
• [3] V. A. Dem'yanenko, On Jeśmanowicz' problem for Pythagorean numbers, Izv. Vyssh. Uchebn. Zaved. Mat. 1965 (5), 52-56 (in Russian).
• [4] A. Grytczuk and A. Grelak, On the equation $a^x+b^y=c^z$, Comment. Math. Prace Mat. 24 (1984), 269-275.
• [5] L.-K. Hua, Introduction to Number Theory, Springer, Berlin, 1982.
• [6] L. Jeśmanowicz, Several remarks on Pythagorean numbers, Wiadom. Mat. (2) 1 (1955/1956), 196-202 (in Polish).
• [7] T. Józefiak, On a conjecture of L. Jeśmanowicz concerning Pythagorean numbers, Comment. Math. Prace Mat. 5 (1961), 119-123 (in Polish).
• [8] Z. Ke, On Pythagorean numbers, J. Sichuan Univ. Nat. Sci. 1958 (1), 73-80 (in Chinese).
• [9] Z. Ke, On Jeśmanowicz' conjecture, ibid. 1958 (2), 81-90 (in Chinese).
• [10] Z. Ke, On the diophantine equation $(2n+1)^x+(2n(n+1))^y= (2n(n+1)+1)^z$, ibid. 1959 (3), 25-34 (in Chinese).
• [11] Z. Ke and Q. Sun, On Pythagorean numbers $2n+1, 2n(n+1)$ and $2n(n+1)+1$, ibid. 1964 (2), 1-12 (in Chinese).
• [12] W.-D. Lu, On the Pythagorean numbers $4n^2-1, 4n$ and $4n^2+1$, ibid. 1959 (2), 39-42 (in Chinese).
• [13] L. J. Mordell, Diophantine Equations, Academic Press, London, 1969.
• [14] V. D. Podsypanin, On a property of Pythagorean numbers, Izv. Vyssh. Uchebn. Zaved. Mat. 1962 (4), 130-133 (in Russian).
• [15] D.-M. Rao, A note on the diophantine equation $(2n+1)^x+(2n(n+1))^y= (2n(n+1)+1)^z$, J. Sichuan Univ. Nat. Sci. 1960 (1), 79-80 (in Chinese).
• [16] W. Sierpiński, On the equation $3^x+4^y=5^z$, Wiadom. Mat. (2) 1 (1955/1956), 194-195 (in Polish).