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Unformatted text preview: 3-176 4 = 242 3-(1870-242 7) 4 = 242 31-1870 4 r = 31 ,s =-4 other solutions are possible but they have to be integers. p35, E5 (i) x = 9 n,y =-8 n , n Z (ii) x =-4 + 9 n,y = 6-8 n , n Z p35, E6(i) x = 5 ,y =-4 p35, E7(i) The gcd of 267 and 112 is 1. x =-39 + 112 n,y = 93-276 n , n Z p35, E8 The gcd of 203 and 119 is 7. So only (iii) has a solution. x = 2 ,y =-3. p36, E20 First of all, since ar + bs is divisible by d , it cannot be any positive number less than d . It is possible to nd r,s s.t. ar + bs = d by the algorithm we learned in this section. 2...
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