# Divides

### Notes on number theory

Notes on number theory Basic fact about division: Exercise 62in Chapter 1 . Let a;b;c;m; and n be integers. Prove that if a divides each of b and c; then a divides nb + mc: Proof.

### Section4.3: Relatively Prime Integers

Theorem 3: For all integers a, b, andc, if a divides bcandgcd(a; b) =1, thena dividesc. Proof: Let a, b, andcbeintegers. Suppose that a divides bc andgcd(a; b) =1.

### FOR IMMEDIATE RELEASE AMERICAN GRACE How Religion Divides and ...

FOR IMMEDIATE RELEASE . AMERICAN GRACE How Religion Divides and Unites Us Robert D. Putnam and David E. Campbell . Date: October 6, 2010 . General Inquiries: Louise Kennedy Converse Louise_Converse@hks.harvard.edu

### Continental Divides in North Dakota and North America

Vol. 30, No. 1 NDGS Newsletter Page 1 Continental Divides in North Dakota and North America by Mark A. Gonzalez To the uninitiated eye, the countryside between Valley ...

### a = bq + r;

If 6 divides the product of integers, does 6 divide one of the factors? 9. Let c (a+ b) and c (a b). Does it follow that c divides a and b?

### Crossing Great Divides

Who We Are Based in Washington, DC, the National Center on Senior Transportation (NCST) is administered by Easter Seals, Inc. in partnership with the National Association of Area Agencies on Aging (n4a) through a cooperative agreement with the U.S. Department of Transportation, Federal Transit ...

### The Cold War Divides the World

Determining Main Ideas Use a chart to list main points about Third World confrontations. TAKING NOTES Country Conflict Cuba Nicaraguga Iran 982 Chapter 33 MAIN IDEA WHY IT MATTERS NOW TERMS & NAMES REVOLUTION The superpowers supported opposing sides in Latin American and Middle Eastern conflicts.

### LATINOS AND BLACKS: What Unites and Divides Us? By Wendy ...

LATINOS AND BLACKS: What Unites and Divides Us? Wendy Conklin The Diversity Factor © 2008 ISSN 1545-2808 Winter 2008 Latinos in the Workplace

### Fostering Dialogue Across Divides

Fostering Dialogue Across Divides A Nuts and Bolts Guide from the Public Conversations Project Maggie Herzig Laura Chasin This guide was made possible through the generous support of the JAMS Foundation.

### Recall: a|b means a divides b ,or b is divisible by

Questions: Why did we avoid division? (Or did we?) What properties of arithmetic are used in the proofs? Discuss the path from definition to assertion to proof.