Let
be given and let N
be the number of solutions
of the equation
where
and
are positive integers. Prove that
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Let $a_1 \geq a_2 \geq a_3 \in \mathbb{Z}^+$ be given and let N$(a_1, a_2, a_3)$ be the number of solutions $(x_1, x_2, x_3)$ of the equation
$$\sum^3_{k=1} \frac{a_k}{x_k} = 1.$$
where $x_1, x_2,$ and $x_3$ are positive integers. Prove that $$N(a_1, a_2, a_3) \leq 6 a_1 a_2 (3 + ln(2 a_1)).$$
Školjka