[KBK]: This exercise asked for a proof that the [[quotient_rep]] procedure in [Fraction Math] terminates after at most 41 iterations of the inner loop, and that at least one argument results in behavior that bad. ---- In case you hadn't noticed, [[quotient_rep]] operates by computing successive convergents to its parameter expressed as a regular continued fraction: 1 ------------------ num = [ a_1, a_2, a_3, ... ] = a_1 + 1 a_2 + ----------- 1 a_3 + ---- . . . The slowest convergence is when all the a_i's are 1, which gives 1 + sqrt( 5 ) num = phi = -------------- 2 In this case the ''p_i'' values in the loop take on the Fibonacci numbers; the 42nd of these exceeds the default value of ''MAXINT''. [[]] ---- [Category Mathematics]