abstract algebra help: In each case find 1 ≦r<b so that b| (ar-1):?
In each case find 1 ≦r<b so that b| (ar-1):
i) a=19 and b= 23
ii) a=113 and b=126
iii) a=89 and b=144
iv) a=16 and b=101
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In each case find 1 ≦r<b so that b| (ar-1):
i) a=19 and b= 23
ii) a=113 and b=126
iii) a=89 and b=144
iv) a=16 and b=101
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Verified answer
Assume that you want to determine the value of r for each part of the problem..
A problem at a time...
b | (ar - 1) means "b divided (ar - 1)". This implies that...
(ar - 1)/b = some quotient..
So we have...
a) (19r - 1) mod 23 = 0
r = 17
b) (113r - 1) mod 126 = 0
r = 29
Good luck!