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Omni-MATH / For each positive integer n, let c(n) be the largest real number such that
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problem
For each positive integer , let be the largest real number such that
\[ c(n) \le \left| \frac {f(a) \minus{} f(b)}{a \minus{} b}\right|\]
for all triples such that
-- is a polynomial of degree taking integers to integers, and
-- are integers with .
Find .
[i]Shaunak Kishore.[/i]Plain-text mathematical notation (without MathML)
For each positive integer n, let c(n) be the largest real number such that
\[ c(n) \le \left| \frac {f(a) \minus{} f(b)}{a \minus{} b}\right|\]
for all triples (f,a,b) such that
--f is a polynomial of degree n taking integers to integers, and
--a,b are integers with f(a)≠f(b).
Find c(n).
[i]Shaunak Kishore.[/i]Original LaTeX notation
For each positive integer $ n$, let $ c(n)$ be the largest real number such that
\[ c(n) \le \left| \frac {f(a) \minus{} f(b)}{a \minus{} b}\right|\]
for all triples $ (f, a, b)$ such that
--$ f$ is a polynomial of degree $ n$ taking integers to integers, and
--$ a, b$ are integers with $ f(a) \neq f(b)$.
Find $ c(n)$.
[i]Shaunak Kishore.[/i]Discussion
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