You may ask the person to encode something by RSA, then you decode it (you have the private key)
OR
To divide two 40-digit integers and give you the decimal result to 100 digits, you then use continued fractions to find the original fraction (reduced)
OR
To compute pq and pr where p,q,r are prime, you then find p,q,r by the Euclidean algorithm (no very deep, but it's the best i've got)
