Question 31
(SWE 3) Let $a_1\ge a_2\ge a_3$ be given positive integers and let $N(a_1,a_2,a_3)$ be the number of solutions $(x_1,x_2,x_3)$ of the equation
$$\frac{a_1}{x_1}+\frac{a_2}{x_2}+\frac{a_3}{x_3}=1,$$
where $x_1,x_2,x_3$ are positive integers. Show that
$$N(a_1,a_2,a_3)\le6a_1a_2(3+\ln(2a_1)).$$
$$\frac{a_1}{x_1}+\frac{a_2}{x_2}+\frac{a_3}{x_3}=1,$$
where $x_1,x_2,x_3$ are positive integers. Show that
$$N(a_1,a_2,a_3)\le6a_1a_2(3+\ln(2a_1)).$$