Restricted Witt algebra and analog of Fermat's Theorem
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I found this interesting result in the work of D. B. Fuchs and T. Evans(2002), and also I have proved this result using Bell polynomials. However, I suppose that there should be more easier solution. Any ideas?
Let $D=ffrac{d}{dx}$ be an operator and $f$ be a function of $x$, so
$D^{p-2}(f)+frac{d^{p-2}}{dx^{p-2}}left(f^{p-1}(x)right)equiv 0;(mod; p)$
abstract-algebra combinatorics number-theory lie-algebras
edited Nov 21 at 12:55
N. F. Taussig
42.9k93254
asked Nov 20 at 11:05
Bakhytbek
4211
add a comment |
up vote
1
down vote
favorite
I found this interesting result in the work of D. B. Fuchs and T. Evans(2002), and also I have proved this result using Bell polynomials. However, I suppose that there should be more easier solution. Any ideas?
Let $D=ffrac{d}{dx}$ be an operator and $f$ be a function of $x$, so
$D^{p-2}(f)+frac{d^{p-2}}{dx^{p-2}}left(f^{p-1}(x)right)equiv 0;(mod; p)$
abstract-algebra combinatorics number-theory lie-algebras
edited Nov 21 at 12:55
N. F. Taussig
42.9k93254
asked Nov 20 at 11:05
Bakhytbek
4211
1
I assume the $f$ in $D$ is the same as in $f$?
– darij grinberg
Nov 20 at 16:31
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I found this interesting result in the work of D. B. Fuchs and T. Evans(2002), and also I have proved this result using Bell polynomials. However, I suppose that there should be more easier solution. Any ideas?
Let $D=ffrac{d}{dx}$ be an operator and $f$ be a function of $x$, so
$D^{p-2}(f)+frac{d^{p-2}}{dx^{p-2}}left(f^{p-1}(x)right)equiv 0;(mod; p)$
abstract-algebra combinatorics number-theory lie-algebras
edited Nov 21 at 12:55
N. F. Taussig
42.9k93254
asked Nov 20 at 11:05
Bakhytbek
4211
I found this interesting result in the work of D. B. Fuchs and T. Evans(2002), and also I have proved this result using Bell polynomials. However, I suppose that there should be more easier solution. Any ideas?
Let $D=ffrac{d}{dx}$ be an operator and $f$ be a function of $x$, so
$D^{p-2}(f)+frac{d^{p-2}}{dx^{p-2}}left(f^{p-1}(x)right)equiv 0;(mod; p)$
abstract-algebra combinatorics number-theory lie-algebras
abstract-algebra combinatorics number-theory lie-algebras
edited Nov 21 at 12:55
N. F. Taussig
42.9k93254
asked Nov 20 at 11:05
Bakhytbek
4211
edited Nov 21 at 12:55
N. F. Taussig
42.9k93254
asked Nov 20 at 11:05
Bakhytbek
4211
edited Nov 21 at 12:55
N. F. Taussig
42.9k93254
edited Nov 21 at 12:55
N. F. Taussig
42.9k93254
edited Nov 21 at 12:55
N. F. Taussig
42.9k93254
42.9k93254
asked Nov 20 at 11:05
Bakhytbek
4211
asked Nov 20 at 11:05
Bakhytbek
4211
asked Nov 20 at 11:05
Bakhytbek
4211
4211
1
I assume the $f$ in $D$ is the same as in $f$?
– darij grinberg
Nov 20 at 16:31
add a comment |
1
I assume the $f$ in $D$ is the same as in $f$?
– darij grinberg
Nov 20 at 16:31
1
1
I assume the $f$ in $D$ is the same as in $f$?
– darij grinberg
Nov 20 at 16:31
I assume the $f$ in $D$ is the same as in $f$?
– darij grinberg
Nov 20 at 16:31
add a comment |
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I assume the $f$ in $D$ is the same as in $f$?
– darij grinberg
Nov 20 at 16:31