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Modern Algebra, MAT 401 Test 3. Show your work (b) 1. Find a solution x E ZOSXsn for the congruence (a) 8x+3= 5 mod 9 8x=l(mo
5. Solve [7][x]-[11] in Z12 6. Prove that for any n 10°=lmod9 7. Given the table below if it is a group complete the table a
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Sokuion: Multiple quesons, os a) plz POst Oer qeons sepahaty Per cheg les are Note: Tere feo atteropring f am Gen data, for t(mod ) th) 8x 1 9 (81- 8Y- For 2 5 3 23 4 31 5 39 41 7 55 63 For 6 63+ 21X 3 I mod 21 solutfor of en Hence a (mod 21) 8x T tGfven data that abel:an prove HOlaba a,be () (ab) a a,s (a) (ab a a,b e 6 tten a beltan be G (ka) a ab)1 Nou, (ab-1 a,b e G c

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