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,
\(3 \%2=1\)
\( 14\%2=0 \)
\( 14\%10=4 \)

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 \( \mathrm{tet}_b(n)\%q = r \)
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 Let \( b>1 \) and \( q>1 \) be integer.