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 A233384 Positive integer solutions (x, y, z), with x <= y <= z, to the equation x*y*z = x + y + z + 2. 0

%I #21 Oct 22 2022 08:08:11

%S 1,2,5,1,3,3,2,2,2

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

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

%H E. Atzema and H. White, <a href="http://books.google.com/books?id=NI2MM3zUVkQC&amp;pg=PA75&amp;dq=%22From+Calculus+to+Computers:+Using+the+Last+200+Years+of+Mathematics+History%22++%22for+mathematicians+looking">Euler on cevians</a>, 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.

%H A. M. Oller-Marcén, <a href="http://www.jstor.org/discover/10.4169/math.mag.86.4.265?uid=3739832">Rational Ratios and Concurrent Cevians</a>, Math. Mag., 86 (2013), 265-269.

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

%K nonn,fini,full

%O 1,2

%A _Jonathan Sondow_, Dec 08 2013

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