Proposihon The cengenunce an=b(modn) has a nduthion ff c@ n Paroof : det d=(n,a). If nEZ Ù o Doleton g then n| cat-b) Since alng dlcan-b) Since dla d aloo divides b. Caonvenely, auppose dlb. by definhan dla s aln. so d 27 = (mod 4) d blomnad ) ano = Requent daufy the masked berhon.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 27E
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Probosition The
congeence
re an=b (modn) Jkas a sdluhan if am)b
Parbot :
det d=(n,a). If REZ Ù o nolution , then n/ can-b) Saince alng dlcan-6)
Bince da
d aloo divides b.
Convrely, suppose dlb. by defiwhan dla a dln. so
b (mod 1)
?
97= (mod 4)
d
ano = blmod n)
Request clavty the marked þertion.
Transcribed Image Text:Probosition The congeence re an=b (modn) Jkas a sdluhan if am)b Parbot : det d=(n,a). If REZ Ù o nolution , then n/ can-b) Saince alng dlcan-6) Bince da d aloo divides b. Convrely, suppose dlb. by defiwhan dla a dln. so b (mod 1) ? 97= (mod 4) d ano = blmod n) Request clavty the marked þertion.
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