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Using the reverse of Euclid's division algorithm compute: (a) Find integers x; y such that 24x...

Using the reverse of Euclid's division algorithm compute:
(a) Find integers x; y such that 24x + 15y = 3
(b) Find integers x; y such that 172x + 20y = 1000
(c) Find integers x; y such that 23x + 17y = 1

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Answer #1

24x +15y= 3 Gy Guelids diislon algosthm 24= 15(1) +g 15 = 9(1)+ 6 9 = 61) +3] 6 = 3(2)+ 0 ged ( 24,15)= 3= 9- 6C1) = 9- (15-O) 23x+ 17y=1. 81 Eudids dinsion lemma, 23 = 1#(1) + G 17= 6(99 t 5 5(1) +0 5= 115)40 gtd (23,17)-l. %3D 1= 6-51) = 6-(14 -6

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