Difference between revisions of "Kuznetsova theorem"

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[[Kuznetsova theorem]] refers to residual of division of [[tetration]] to integer base by any integer number.
 
 
==[[Kuznetsova theorem]]==
 
==[[Kuznetsova theorem]]==
   
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\( \mathrm{tet}_b(n)\%q = r \)
 
\( \mathrm{tet}_b(n)\%q = r \)
 
 
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Let \( b>1 \) and \( q>1 \) be integer.
 
Let \( b>1 \) and \( q>1 \) be integer.
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for any integer \(n > Q \), there exist positive integer \( a \) such that \( \mathrm{tet}_b(n)\! =\! q a\! +\!r \)
 
for any integer \(n > Q \), there exist positive integer \( a \) such that \( \mathrm{tet}_b(n)\! =\! q a\! +\!r \)
 
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== Notations==
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Here symbol tet veters to [[tetration]]. The base is indicated as subscript.
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Character % refers to residual of division of the number at left (treated as numerator) by number at right (intepreted as denominator).
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For example, <br>
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\(3 \%2=1\)<br>
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\( 14\%2=0 \)<br>
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\( 14\%10=4 \)
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==References==
 
==References==
 
<references/>
 
<references/>

Latest revision as of 20:23, 23 January 2020

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

References

Keywords

Integer number, Tartaria, Tartaria.Math, Tetration, Yulya Kuznetsova