Exercise 2.1.7 (First examples, part 7)

Question

Show that if $f(x)$ is a polynomial with integral coefficients and if $f(a) \equiv k \pmod m$, then $f(a+tm) \equiv k \pmod m$ for every integer $t$.

Richard Ganaye · Accepted Answer

\begin{proof} Since $a + tm \equiv a \pmod m$, by theorem 2.2,
$$f(a+tm) \equiv f(a) \pmod m.$$
Since $f(a) \equiv k \pmod m$,
$$f(a+tm) \equiv k \pmod m.$$
\end{proof}

Exercise 2.1.7 (First examples, part 7)

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Exercise 2.1.7 (First examples, part 7)

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