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*. []