Difference between revisions of "Kuznetsova theorem"

Revision as of 20:22, 23 January 2020

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

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:

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

Here symbol tet veters to tetraton. 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,
\(3 \%2=1\)
\( 14\%2=0 \)
\( 14\%10=4 \)

@@ Line 21: / Line 21: @@
 For example, <br>
-\(3 \!2=1\)<br>
+\(3 \%2=1\)<br>
 \( 14\%2=0 \)<br>
 \( 14\%10=4 \)
 ==References==