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  • Proceedings of the Edinburgh Mathematical Society, Volume 40, Issue 1
  • February 1997, pp. 1-17

Two more representation problems

  • Andrew Bremner (a1) and Richard K. Guy (a2)
  • DOI:
  • Published online: 01 February 1997

We discuss the problem of finding those integers which may be represented by (x + y + z)3/xyz, and also those which may be represented by x/y + y/z + z/x, where x, y, z are integers. For example,

satisfy (x + y + z)3/(xyz) = -47, and

satisfy x/y + y/z + z/x = -86.

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2.Andrew Bremner , Richard K. Guy and Richard J. Nowakowski , Which integers are representable as the product of the sum of three integers with the sum of their reciprocals? Math. Comput. 61 (1993) (Lehmer Memorial issue), 117130; MR 93k: 11021.

5.Maurice Craig , Integer Values of Σ(X2/yz), J. Number Theory 10 (1978), 6263.

6.Erik Dofs , On some classes of homogeneous ternary cubic Diophantine equations, Ark. Mat. 13 (1975), 2972.

8.Richard K. Guy , Problem 10382, Amer. Math. Monthly 101 (1994), 473; pre-publication solutions by Arthur Baragar and Brian Peterson.

12.S. P. Mohanty , A system of cubic Diophantine equations, J. Number Theory 9 (1977), 153159.

15.E. Thomas and A. T. Vasquez , Diophantine equations arising from cubic number fields, J. Number Theory 13 (1981), 398414.

16.Andrew Wiles , Modular elliptic curves and Fermat's Last Theorem, Ann. of Math. (2) 141 (1995), 443551.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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