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MathNet 2022-part-06 — 196 problems (EN–VI) Question 134

Math Olympiad Vault · MathNet 2022-part-06 — 196 problems (EN–VI)

Question 134

The function $f(x)$ is of the form $a x^{2}+b x+c$ for some integers $a, b$, and $c$. Given that
$$
\begin{aligned}
\{f(177883), f(348710), & f(796921), f(858522)\} \\
= & \{1324754875645,1782225466694,1984194627862,4388794883485\}
\end{aligned}
$$
compute $a$.