Okay, so here's another one...
 

... for all you number crunchers out there.

Maybe you already heard about "minimal primes": [URL]http://primes.utm.edu/glossary/page.php?sort=MinimalPrime[/URL]

So far, so easy.

Now, what about the minimal set of square numbers?
Here's how it starts:
1
4
9
25
36
576
676
7056
80656
665856
2027776
2802276
22282727076
77770707876
78807087076
7888885568656
8782782707776
72822772707876
...

- How many others can you find?
- Will this list come to an end eventually?

An easier problem would use the nonnegative squares rather than the positive squares.

[QUOTE=mart_r;157999]- Will this list come to an end eventually?[/QUOTE]

Lothaire's result implies that the list is finite, so yes.

[quote=CRGreathouse;158025]An easier problem would use the nonnegative squares rather than the positive squares.[/quote]

Where's the difference? Include zero?

[QUOTE=mart_r;158056]Where's the difference? Include zero?[/QUOTE]

Sure. The list would start 0, 1, 4, 9, 25, 36, 576, 676, 665856, ...

interesting...i'll work on it when i have time