Saints and Scoundrels and Two Theorems That Are Really the Same

The Chinese remainder theorem and the polynomial interpolation theorem are foundational theorems of number theory and numerical analysis, respectively. These two theorems are special cases of a construct in a more general setting and we describe a scenario—namely, two back-to-back classes—in which s...

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Bibliographic Details
Published in:	The College mathematics journal Vol. 46; no. 5; pp. 326 - 334
Main Author:	Brown, Ezra
Format:	Journal Article
Language:	English
Published:	Washington Mathematical Association of America 01-11-2015 Taylor & Francis Ltd
Subjects:	Degrees of polynomials Integers Interpolation Mathematical congruence Mathematical constants Mathematical theorems Number theory Numerical analysis Polynomials Real numbers Remainders Theorems
Online Access:	Get full text
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Summary:	The Chinese remainder theorem and the polynomial interpolation theorem are foundational theorems of number theory and numerical analysis, respectively. These two theorems are special cases of a construct in a more general setting and we describe a scenario—namely, two back-to-back classes—in which students can discover this fact. We end by describing that general setting, in which the key idea is an ability to write 1 in a special way.
ISSN:	0746-8342 1931-1346
DOI:	10.4169/college.math.j.46.5.326