A233384 Positive integer solutions (x, y, z), with x <= y <= z, to the equation x*y*z = x + y + z + 2.

1, 2, 5, 1, 3, 3, 2, 2, 2

Offset

1,2

Comments

For applications of the equation to Euler's theorem on cevians of a triangle, see Atzema and H. White (2005) and Oller-Marcén (2013).

Links

Table of n, a(n) for n=1..9.

E. Atzema and H. White, Euler on cevians, in "From Calculus to Computers: Using the Last 200 Years of Mathematics History in the Classroom", A. Shell-Gellasch and D. Jardine, eds., Cambridge University Press, 2005.

A. M. Oller-Marcén, Rational Ratios and Concurrent Cevians, Math. Mag., 86 (2013), 265-269.

Example

1*2*5 = 10 = 1+2+5+2, 1*3*3 = 9 = 1+3+3+2, 2*2*2 = 8 = 2+2+2+2.

Crossrefs

Sequence in context: A091953 A228824 A011456 * A186692 A296847 A100084

Adjacent sequences: A233381 A233382 A233383 * A233385 A233386 A233387

Keyword

nonn,fini,full

Author

Jonathan Sondow, Dec 08 2013

Status

approved