# Reducing numbers

There is something going through my mind recently.
is it possible to reduce any number to the following form:
x^n +y , and -x+1<y<x-1?? x isn't necessarily prime
or better something like this x^n +y where y=+1 or -1
I tried many numbers, so far I can't see a contradiction to these 2 rules I stated, or maybe there is one, but can't really see it.
I want to see if it's possible to reduce a very very big number, to a simpler form, like the 2 i stated above.
example:(I don't know if this is correct)
1...million zero...1
it should be reduced to this 1000^1000 +1

Last edited:

matt grime
Homework Helper
One assume you do not consider n=1 acceptable.

If not then you obviously can't have the extra condition that y=+/-1, as not every number is one more or less than a perfect power.

what about the first way I thought of ?
x^n +y , and -x+1<y<x-1 not possible too ?

matt grime