I'm thinking of a number, x, whose last 3 digits are somewhere between 400 and 500.

You could probably guess from those digits that it might be a square or a cube, but in fact it turns out to be both, and in fact the smallest possible such number.

What are the prime factors of x?

Extra credit: feeling adventurous, I next computed the smallest number, y, having the same last 3 digits, that was a seventh power, as well as a square and a cube.

What are the prime factors of y?

Well, I have agreement with Charlie and Jer on the first part.

As I wade through Charlie's commentary I still agree with him about 3^1512.  I hadn't considered there to be anything less however.

This was a very interesting exercise.

Posted by brianjn on 2013-01-30 17:51:17