Originally Posted by

**Bruno J.** We have the identity

which shows that it's impossible for the sequence

to be eventually constantly equal to -1. If it is eventually constantly equal to 1, let

be the greatest integer such that

. Then by hypothesis

and then

, contradicting the choice of

.

nice!

just note that before choosing the greatest integer

with

you should mention that basically the set

is non-empty.

this, of course, is trivial in our case because

but it becomes absolutely non-trivial if we replace

with an arbitrary non-zero integer

finally the identity you used can be extended. in general we have:

You always have nice problems, NonCommLion.

thanks! i like my new user name: NCL! it could also stand for Normal CLosure!

Where do you get them from?

here and there!