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?

Thanks broll.  I'll give what you offer some thought in the next few days, but frankly I'm still trying to  come to grips with "endings resulting from MOD(x)".  I've never been exposed to that until recently at Perplexus.  Good testimonial for the site, yes?

Wolframalpha?  What is that? Does it require a subscription, or is it one of the download products?

Posted by brianjn on 2013-01-31 02:14:31