Difference between revisions of "Kuznetsova theorem"
| Line 13: | Line 13: | ||
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 \( \mathrm{tet}_b(n)\! =\! q a\! +\!r \) |
||
!--> |
!--> |
||
| + | |||
| + | == notations== |
||
| + | |||
| + | 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, <br> |
||
| + | \(3 \!2=1\)<br> |
||
| + | \( 14\%2=0 \)<br> |
||
| + | \( 14\%10=4 \) |
||
| + | |||
| + | |||
==References== |
==References== |
||
<references/> |
<references/> |
||
Revision as of 20:21, 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 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,
\(3 \!2=1\)
\( 14\%2=0 \)
\( 14\%10=4 \)
References
Keywords
Integer number, Tartaria, Tartaria.Math, Tetration, Yulya Kuznetsova
