# Difference between revisions of "Kuznetsova theorem"

Kuznetsova theorem refers to residual of division of tetration to integer base by any integer number.

## Kuznetsova theorem

Let $$b>1$$ and $$q>1$$ be integers.

Then, there exist positive integer $$Q$$ and integer $$r$$ such that for any integer $$n > Q$$ the equation holds:

$$\mathrm{tet}_b(n)\%q = r$$

## Notations

Here symbol tet veters to tetration. The base is indicated as subscript.

Character % refers to residual of division of the number at left (treated as numerator) by number at right (intepreted as denominator).

For example,
$$3 \%2=1$$
$$14\%2=0$$
$$14\%10=4$$