The following algorithm can be applied to a list of fractions and an integer input. You go down the list and multiply the input by the first fraction that will result in an integer. Taking this product as the new input, you repeat, using the same list of fractions. The algorithm ends when none of the fractions will result in an integer.

For example, if the list of fractions is {5/6, 5/2, 5/3}, then inputting an integer 2^a * 3^b will result in 5^max(a,b). A more complicated example: inputting 2^a * 3^b into {7/11, 11/(3*7), 1/7, (5*7)/2, 3/5} will result in 3^a (if a>0).

Find a list of fractions such that inputting an integer 2^a * 3^b will result in 5^ab.

How about a list that, when the input is 2^a * 3^b, results in 5^{a^b} (with b>0)?

(In reply to First question by Gamer)

According to your "algorithm" I think your (7*11)/13 should be 11/(7*13) and your (3*11)/7 should be 11/(7*3).

However, I think your solution is off.  I think you are getting 5^(a*(b+1))

The problem is that if there are no 3s you are making 5s anyway.

Posted by Joel on 2006-11-21 23:03:41