números y griego-romano

Siguin a_{1},...,a_{n}€R^{>0} & m_{1},...,m_{n}€N ==> ...

... [Ek][Es][ ( k€N & s€N ) & 0 [< a_{1}m_{1}+...+a_{n}m_{n}+(-k) < s ]

Es defineish: k = [a_{1}]·m_{1}+...+[a_{n}]·m_{n}

Es defineish: s€N & s > m_{1}+...+m_{n}

0 [< a_{1}m_{1}+...+a_{n}m_{n}+(-k) < s

Griego-Romano:

parlare-proika

parlamu-koika

parlái-koika

parlan-proika

havere-proika parlatu-prom

havemu-koika parlatu-prom

havéi-koika parlatu-prom

haven-proika parlatu-prom

vare-proika parlare-prom

varamu-koika parlare-prom

varai-koika parlare-prom

varen-proika parlare-prom

ishtéipe <==> q-este

ishtéipa <==> q-esta

ishtéipos <==> q-estos

ishtéipas <==> q-estas

ishéipe <==> q-ese

ishéipa <==> q-esa

ishéipos <==> q-esos

ishéipas <==> q-esas

yo sere-proika un óptico mayoika.

yo sere-proika un óptico menoika.

l'óptico mayoika havere-proika parlatu-prom.

l'óptico menoika havere-proika parlatu-prom.

yo querere-proika un gelatu-prom de lemon-kale.

yo querere-proika un gelatu-prom de oranji-kale.

te gustare-proika mi peinato-prom?.

me gustare-proika tu peinato-prom.

tú querere-proika fachere-prom un café-kale con micu?.

yo querere-proika fachere-prom un café-kale con ticu.

tú querere-proika cantare-prom una cantzoude con micu?.

yo querere-proika cantare-prom una cantzoude con ticu.

a = ( ( p_{1} )^{m_{1}} )·...·( ( p_{n} )^{m_{n}} )

f(a) = a·( 1+(-1)·(1/p_{1}) )·...·( 1+(-1)·(1/p_{n}) )

f(1) = 1

teorema:

f(2^{n}) = 2^{n+(-1)}

teorema:

f(p) = p+(-1)

f(p^{m_{k}}) = p^{m_{k}}+(-1)·p^{m_{k}+(-1)}

teorema:

sum[ ( p_{1} )^{k} | a ][ f(( p_{1} )^{k}) ]·...·sum[ ( p_{n} )^{k} | a ][ f(( p_{n} )^{k}) ] = a

Demostrció:

( 1+f(p_{1})+...+f(( p_{1} )^{m_{1}}) )·...·( 1+f(p_{1})+...+f(( p_{n} )^{m_{n}}) ) = ...

... ( ( p_{1} )^{m_{1}} )·...·( ( p_{n} )^{m_{n}} ) = a

g_{n}(a) = sum[ x_{1}·...·x_{n} = a ][ n_{k} succesions que són solució a la ecuació ]

g_{n}(p) = n

g_{n}(p^{k}) = [ n // k ]

p111 || 1p11 || 11p1 || 111p = 4 = g_{4}(p)

pp11 || 1pp1 || 11pp || p11p || p1p1 || 1p1p = 6 = g_{4}(p^{2})

ppp1 || 1ppp || p1pp || pp1p = 4 = g_{4}(p^{3})

ppp11 || 1ppp1 || 11ppp || p11pp || pp11p || ...

... pp1p1 || 1pp1p || p1pp1 || 1p1pp || p1p1p = 10 = g_{5}(p^{3})

teorema:

lim[n-->oo][ g_{n}(p^{k})/2^{n} ] < 1

demostració:

g_{n}(p^{k}) = [ n // k ] < (1+1)^{n} = 2^{n}

n! = n^{n}+O( n^{n} )

(-1) [< ( n!/n^{n} )+(-1) [< 0

n! = 1·2·...·n [< n·...(n)...·n = n^{n}

ln(n) = n+O(n)

(-1) [< ( ln(n)/n )+(-1) < 0

n < e^{n} = 1+n+(1/2!)·n^{2}+...

ln(n) < n

a = ( p_{1} )^{m_{1}}·...·( p_{n} )^{m_{n}}

Si [Am_{k}][ m_{k} = 1 ] ==> h(a) = (-1)^{n}

Si [Em_{k}][ m_{k} >] 2 ] ==> h(a) = 0

h(1) = 0

Si [An][ n >] 2 ==> [Ed][ d | a & 0 [< d [< a^{(1/n)} ] ] ==> h(a) = 0

a = d^{n}·k

f(a) = a·prod[ k = 1 --> n ][ ( ( p_{k}+h(p_{k}) )/p_{k} ) ]

h(p_{k}) = (-1)

[An][ n >] 2 ==> h( ( f(p) )^{n} ) = 0

( f(p) )^{n} = ( p+(-1) )^{n} = ( k_{1} )^{n}·...·( k_{s} )^{n}

punts enters en una regió circular:

f( x^{2}+y^{2} [< n^{2} ) = 2·(n+1)·(n+2)+(-4)·(n+1)+1

<0,0>

<1,0> & <0,1>

<2,0> & <1,1> & <0,2>

n = 0 ==> f( x^{2}+y^{2} [< 0^{2} ) = 1

n = 1 ==> f( x^{2}+y^{2} [< 1^{2} ) = 5

n = 2 ==> f( x^{2}+y^{2} [< 2^{2} ) = 13

punts enters en una regió cuadrada:

f( |x| [< n & |y| [< n ) = 4·(n+1)^{2}+(-4)·(n+1)+1

<0,0>

<1,0> & <1,1> & <0,1>

<2,0> & <2,1> & <2,2> & <1,2> & <0,2>

n = 0 ==> f( |x| [< 0 & |y| [< 0 ) = 1

n = 1 ==> f( |x| [< 1 & |y| [< 1 ) = 9

n = 2 ==> f( |x| [< 2 & |y| [< 2 ) = 25

vare-proika apestare-prom,

en eseipa follata-prom.

vare-pruika apestare-prum,

en isheipa follata-prum.