Difference between revisions of "Kuznetsova theorem"
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(Created page with " ==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 e...") |
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| + | [[Kuznetsova theorem]] refers to residual of division of [[tetration]] to integer base by any integer number. |
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==[[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== |
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<references/> |
<references/> |
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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