A note on the Diophantine equation a x + b y = c z

Zhenfu Cao

Acta Arithmetica (1999)

  • Volume: 91, Issue: 1, page 85-93
  • ISSN: 0065-1036

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Zhenfu Cao. "A note on the Diophantine equation $a^x + b^y = c^z$." Acta Arithmetica 91.1 (1999): 85-93. <http://eudml.org/doc/207341>.

@article{ZhenfuCao1999,
author = {Zhenfu Cao},
journal = {Acta Arithmetica},
keywords = {exponential Diophantine equation; exponential diophantine equation},
language = {eng},
number = {1},
pages = {85-93},
title = {A note on the Diophantine equation $a^x + b^y = c^z$},
url = {http://eudml.org/doc/207341},
volume = {91},
year = {1999},
}

TY - JOUR
AU - Zhenfu Cao
TI - A note on the Diophantine equation $a^x + b^y = c^z$
JO - Acta Arithmetica
PY - 1999
VL - 91
IS - 1
SP - 85
EP - 93
LA - eng
KW - exponential Diophantine equation; exponential diophantine equation
UR - http://eudml.org/doc/207341
ER -

References

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  2. [2] Z. F. Cao, On the Diophantine equation a x 2 + b y 2 = p z , J. Harbin Inst. Tech. 23 (1991), 108-111. Zbl0971.11512
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  7. [7] T. Hadano, On the Diophantine equation a x = b y + c z , Math. J. Okayama Univ. 19 (1976/77), 25-29. Zbl0349.10012
  8. [8] M. H. Le, On Jeśmanowicz' conjecture concerning Pythagorean numbers, Proc. Japan Acad. Ser. A Math. Sci. 72 (1996), 97-98. Zbl0876.11013
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  15. [15] R. Scott, On the equations p x - b y = c and a x + b y = c z , J. Number Theory 44 (1993), 153-165. Zbl0786.11020
  16. [16] Q. Sun and X. M. Zhou, On the Diophantine equation a x + b y = c z , Chinese Sci. Bull. 29 (1984), 61 (in Chinese). 
  17. [17] K. Takakuwa, On a conjecture on Pythagorean numbers, III, Proc. Japan Acad. Ser. A Math. Sci. 69 (1993), no. 9, 345-349. Zbl0822.11025
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  19. [19] K. Takakuwa and Y. Asaeda, On a conjecture on Pythagorean numbers, II, Proc. Japan Acad. Ser. A Math. Sci. 69 (1993), no. 8, 287-290. 
  20. [20] N. Terai, The Diophantine equation a x + b y = c z , Proc. Japan Acad. Ser. A Math. Sci. 70 (1994), 22-26. Zbl0812.11024
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