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Unformatted text preview: × 3176 × 4 = 242 × 3(1870242 × 7) × 4 = 242 × 311870 × 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 = 68 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 = 93276 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 ﬁnd r,s s.t. ar + bs = d by the algorithm we learned in this section. 2...
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 Spring '08
 BILLERA
 Math, Algebra, Prime number, Erdős–Woods number, inductive step, p35

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