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Since a−x +1 ∣ ax +b and a− x+1 ∣ a(a −x+ 1) we have a −x +1 ∣ (ax +b)+ (a2 −ax +a) = a2 + a+ b So x = a −d +1 where d divides a2 + a+b. Suppose b = 0. Then f (0) = −1/b and if f is self inverse 0 =
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