Question 42
Let $n$ be a positive integer. Show that there exist positive integers $a$ and $b$ such that:
$$
\frac{a^{2}+a+1}{b^{2}+b+1}=n^{2}+n+1
$$
$$
\frac{a^{2}+a+1}{b^{2}+b+1}=n^{2}+n+1
$$
MathNet 2017-part-04 — 176 problems (EN–VI) Question 42
Math Olympiad Vault · MathNet 2017-part-04 — 176 problems (EN–VI)