First problem. Solved using modulus.

I am noticing a pattern in the 3||5 modulo. E.g..

3,5,6,9,10,12,15,18,20,21,24,25,28,30

this creates a pattern of 2,1,3,1,2,3...

I wonder if I can use this somehow?
A rather ugly solution to problem 2

A rather ugly solution that involves calculating all Fib' values up to a
certain point, and then returning them as an array of values. The reject
method is used to return an array of even numbers, and we then use inject to
perform a summation.
Progress for problem 3: prime factorization.

The idea here is to generate a list of prime factors really quickly (thank
you, sieve), and then iterate over a number, finding out what prime it's
divisible by, and then starting over again.
This solution is going to be slow as hell, but it's the best thing I can think
of at this very moment.