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In [1], A. Bremner and R. K. Guy discuss the problem of findin8 integers which maybe represented by (x+y+z)3/xyz where X,Y,Z are integers. To this end, they present tables ofsolutions for integers n in the range −200≤n≤200 and offer several parametric solutions whichinvolve both positive and negative integers. We present four infinite families of solutions whichinvolve only positive intesers. Furthermore, these families contain sequences that are generatedby linearly recursive relations

international journal of mathematics and mathematical sciences

Integers representable by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$(x + y + z)^3/xyz$"><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:mi>y</mml:mi><mml:mo>+</mml:mo><mml:mi>z</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mn>3</mml:mn></mml:msup><mml:mo>/</mml:mo><mml:mi>x</mml:mi><mml:mi>y</mml:mi><mml:mi>z</mml:mi></mml:math>

Integers representable by(x+y+z)3/xyz