This isn't much fun, but some of you with access to algebra manipulation systems may be able to help. Etienne Garnier has pointed out what must be a mistake in D13 of UPINT. I'm not able to access the relevant paper or even a review thereof, so could someone check what value of z (if any) should replace the one given below in the solution of the equation x1^x1 * x2^x2 * ... * xk^xk = z^z ? [the exponent of k in z is less than that of x_1 and there is no factor k^n-1 at all] Many thanks in anticipation. R. Claude Anderson conjectured that the equation $w^wx^xy^y=z^z$ has no solutions with $1<w<x<y<z$, but Chao Ko & Sun Qi had earlier found an infinity of counterexamples to a generalization of the conjecture to any number of variables: x_1 = k^{k^n(k^{n+1}-2n-k)+2n}(k^n-1)^{2(k^n-1)} x_2 = k^{k^n(k^{n+1}-2n-k)}(k^n-1)^{2(k^n-1)+2} x_3 = ... = x_k = k^{k^n(k^{n+1}-2n-k)+n}(k^n-1)^{2(k^n-1)+1} z = k^{k^n(k^{n+1}-2n-k)+n+1} ??????? Chao Ko & Sun Qi, On the equation $\prod^k_{i=1}x_i^{x_i}$, {\it J.\ Sichuan Univ.}, {\bf2}(1964) 5--9. [I may even have got the title of the paper wrong, since an ``= z^z'' seems to be missing.]