Difference between revisions of "Kuznetsova theorem"

From TORI
Jump to navigation Jump to search
 
(3 intermediate revisions by the same user not shown)
Line 7: Line 7:
   
 
\( \mathrm{tet}_b(n)\%q = r \)
 
\( \mathrm{tet}_b(n)\%q = r \)
 
 
<!--
 
<!--
 
Let \( b>1 \) and \( q>1 \) be integer.
 
Let \( b>1 \) and \( q>1 \) be integer.
Line 14: Line 13:
 
!-->
 
!-->
   
== notations==
+
== Notations==
   
Here symbol tet veters to [[tetraton]]. The base is indicated as subscript.
+
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).
 
Character % refers to residual of division of the number at left (treated as numerator) by number at right (intepreted as denominator).
   
 
For example, <br>
 
For example, <br>
\(3 \!2=1\)<br>
+
\(3 \%2=1\)<br>
 
\( 14\%2=0 \)<br>
 
\( 14\%2=0 \)<br>
 
\( 14\%10=4 \)
 
\( 14\%10=4 \)
 
   
 
==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