TY - JOUR
T1 - Two more representation problems
AU - Bremner, Andrew
AU - Guy, Richard K.
N1 - Funding Information:
* Supported by Nat. Sci. Engg. Res. Council of Canada grant A-4011.
PY - 1997
Y1 - 1997
N2 - 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, x = -3888953655693309094309277243253295616000, y = 870614350109377939730940722158565152629, z = -211788680591112853611774198484237121509 satisfy (x + y + z)3/(xyz) = -47, and x = 10695607136243980529530429582617991136107507407713992824, y = -123256655541019041417443728014061733054947136623569984, z = 8446121230200308492574953446465639841507828834632079329 satisfy x/y + y/z + z/x = -86.
AB - 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, x = -3888953655693309094309277243253295616000, y = 870614350109377939730940722158565152629, z = -211788680591112853611774198484237121509 satisfy (x + y + z)3/(xyz) = -47, and x = 10695607136243980529530429582617991136107507407713992824, y = -123256655541019041417443728014061733054947136623569984, z = 8446121230200308492574953446465639841507828834632079329 satisfy x/y + y/z + z/x = -86.
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U2 - 10.1017/s0013091500023397
DO - 10.1017/s0013091500023397
M3 - Article
AN - SCOPUS:33747394312
SN - 0013-0915
VL - 40
SP - 1
EP - 17
JO - Proceedings of the Edinburgh Mathematical Society
JF - Proceedings of the Edinburgh Mathematical Society
IS - 1
ER -