Let m, q and p be a positive integers. Prove that among any group of qmp +1 (not necessarily consecutive) integers, there are at least (pm+1) with exactly the same reminder when they are divided by q.
Let m, q and p be a positive integers. Prove that among any group of qmp +1 (not necessarily consecutive) integers, there are at least (pm+1) with exactly the same reminder when they are divided by q.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.5: Normal Subgroups
Problem 38E: Let n be appositive integer, n1. Prove by induction that the set of transpositions...
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Let m, q and p be a positive integers.
Prove that among any group of qmp +1 (not necessarily consecutive) integers, there are at least (pm+1) with exactly the same reminder when they are divided by q.
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