2. Let a €R and n € Zs0. Show that of the numbers a, 2a,..., (n – 1)a there is one whosedistance from an integer is at most 1/n.3. 20 distinct positive integers all < 70 have been given. Show that among their pairwisedifferences there are (at least) 4 equal numbers.4. Let G be a group with its operation denoted by . Suppose o : N G is a function withthe following pronertv: for every a.he N. we have

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 17E: let Un be the group of units as described in Exercise16. Prove that [ a ]Un if and only if a and n...

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2. Let a € R and n € Z0. Show that of the numbers a, 2a, distance from an integer is at most 1/n. ..., (n- 1)a there is one