teorema de las no ternas pitagóricas de fermat

Teorema de Fermat:

x^{n+1}+y^{n+1} = m^{n+1}

x(t) = m·( cos(t) )^{( 2/(n+1) )}

y(t) = m·( sin(t) )^{( 2/(n+1) )}

m^{n+1}·( cos(t) )^{2}+m^{n+1}·( sin(t) )^{2} = ...

... m^{n+1}·( ( cos(t) )^{2}+( sin(t) )^{2} ) = m^{n+1}

No tiene soluciones enteras para: n > 1

(p/q) = cos(t) & (u/v) = sin(t)

m^{n+1}·(p/q)^{2} = ( m·(p/q)^{2/(n+1)} )^{n+1}

m^{n+1}·(u/v)^{2} = ( m·(u/v)^{2/(n+1)} )^{n+1}

Si n = 1 ==>

q = m & p < m

v = m & u < m

x^{n+1}+y^{n+1} = n^{n+1}

x(t) = cos[n](t) = n·( cos(t) )^{( 2/(n+1) )}

y(t) = sin[n](t) = n·( sin(t) )^{( 2/(n+1) )}

Homología elíptica:

cos[n+1](t) = ( (n+1)/n )·( cos[n](t) )^{( (n+1)/(n+2) )}

sin[n+1](t) = ( (n+1)/n )·( sin[n](t) )^{( (n+1)/(n+2) )}

cos[1](t) --->...(n)...---> cos[n](t)

sin[1](t) --->...(n)...---> sin[n](t)

x^{(1/(n+1))}+y^{(1/(n+1))} = n^{(1/(n+1))}

x(t) = cos[(1/n)](t) = n·( cos(t) )^{( 2·(n+1) )}

y(t) = sin[(1/n)](t) = n·( sin(t) )^{( 2·(n+1) )}

Co-Homología elíptica:

cos[(1/(n+1))](t) = ( (n+1)/n )·( cos[(1/n)](t) )^{( (n+2)/(n+1) )}

sin[(1/(n+1))](t) = ( (n+1)/n )·( sin[(1/n)](t) )^{( (n+2)/(n+1) )}

cos[(1/1)](t) --->...(n)...---> cos[(1/n)](t)

sin[(1/1)](t) --->...(n)...---> sin[(1/n)](t)

Teorema de Fermat-Wiles:

x^{n+1}+y^{n+1} = ( k_{n}·n )^{n+1} 

No tiene soluciones enteras para: n > 1.

Sea k_{i}€Z ==>

k_{1}·f_{1}(t) --->...(n)...----> k_{n}·f_{n}(t)

k_{1}·g_{1}(t) --->...(n)...----> k_{n}·g_{n}(t)

f_{n+1} = F( f_{n}(t) ) & F(x)€I

g_{n+1} = G( g_{n}(t) ) & G(y)€I

x(t) = k_{n}·n·( cos(t) )^{( 2/(n+1) )}

y(t) = k_{n}·n·( sin(t) )^{( 2/(n+1) )}

Si n = 1 ==>

k_{n} = 5m

cos(t) = (3/5)

sin(t) = (4/5)

Teorema de Fermat-Wiles-Inverso:

x^{(1/(n+1))}+y^{(1/(n+1))} = ( k_{n}·n )^{(1/(n+1))}

No tiene soluciones enteras para: n > 1. 

Sea k_{i}€Z ==>

k_{1}·f_{1}(t) --->...(n)...----> k_{n}·f_{n}(t)

k_{1}·g_{1}(t) --->...(n)...----> k_{n}·g_{n}(t)

f_{n+1} = F( f_{n}(t) ) & F(x)€I

g_{n+1} = G( g_{n}(t) ) & G(y)€I

x(t) = k_{n}·n·( cos(t) )^{( 2·(n+1) )}

y(t) = k_{n}·n·( sin(t) )^{( 2·(n+1) )}

Si n = 1 ==>

k_{n} = 4m

cos(t) = ( 2^{(1/2)}/2 )

sin(t) = ( 2^{(1/2)}/2 )

x^{p(n+1)}+y^{p(n+1)} = n^{mp(n+1)}

x(t) = cos[pn:mpn](t) = n^{m}·( cos(t) )^{( 2/(p(n+1)) )}

y(t) = sin[pn:mpn](t) = n^{m}·( sin(t) )^{( 2/(p(n+1)) )}

Homología deformable:

cos[pn+p:mpn+mp](t) = ( (n+1)/n )^{m}·( cos[pn:mpn](t) )^{( (n+1)/(n+2) )}

sin[pn+p:mpn+mp](t) = ( (n+1)/n )^{m}·( sin[pn:mpn](t) )^{( (n+1)/(n+2) )}

cos[p:mp](t) --->...(n)...---> cos[pn:mpn](t)

sin[p:mp](t) --->...(n)...---> sin[pn:mpn](t)

x^{(1/(p(n+1)))}+y^{(1/(p(n+1)))} = n^{(1/(mp(n+1)))}

x(t) = cos[(1/(pn)):(1/(mpn))](t) = n^{(1/m)}·( cos(t) )^{( 2·p(n+1) )}

y(t) = sin[(1/(pn)):(1/(mpn))](t) = n^{(1/m)}·( sin(t) )^{( 2p(n+1) )}

Co-Homología deformable:

cos[(1/(pn+p)):(1/(mpn+mp))](t) = ...

... ( (n+1)/n )^{(1/m)}·( cos[(1/(pn)):(1/(mpn))](t) )^{( (n+2)/(n+1) )}

sin[(1/(pn+p)):(1/(mpn+mp))](t) = ...

... ( (n+1)/n )^{(1/m)}·( sin[(1/(pn)):(1/(mpn))](t) )^{( (n+2)/(n+1) )}

cos[(1/p):(1/(mp)](t) --->...(n)...---> cos[(1/(pn)):(1/(mpn)](t)

sin[(1/p):(1/(mp)](t) --->...(n)...---> sin[(1/(pn)):(1/(mpn)](t)

Teorema:

x^{p(n+1)}+y^{p(n+1)} = ( k_{n}·n )^{mp(n+1)} 

No tiene soluciones enteras para: ( n != 1 || p != 1 || m != 1).

Tiene soluciones enteras para: ( n = 1 & p = 1 & m = 1 ).

Sea k_{i}€Z ==>

k_{1}·f_{1}(t) --->...(n)...----> k_{n}·f_{n}(t)

k_{1}·g_{1}(t) --->...(n)...----> k_{n}·g_{n}(t)

f_{n+1} = F( f_{n}(t) ) & F(x)€I

g_{n+1} = G( g_{n}(t) ) & G(y)€I

x^{p(n+1)}+y^{q(n+1)} = n^{n+1}

x(t) = cos[pn:qn](t) = n^{(1/p)}·( cos(t) )^{( 2/(p(n+1)) )}

y(t) = sin[qn:pn](t) = n^{(1/q)}·( sin(t) )^{( 2/(q(n+1)) )}

Homología elíptica:

cos[p(n+1):q(n+1)](t) = ( (n+1)/n )^{(1/p)}·( cos[pn:qn](t) )^{( (n+1)/(n+2) )}

sin[q(n+1):p(n+1)](t) = ( (n+1)/n )^{(1/q)}·( sin[qn:pn](t) )^{( (n+1)/(n+2) )}

cos[p:q](t) --->...(n)...---> cos[pn:qn](t)

sin[q:p](t) --->...(n)...---> sin[qn:pn](t)