teoría de díjits

( <a_{1},a_{2}> = <a_{2},a_{1}> & a_{1}+a_{2}=8 ) <==> ( a_{1}=4 & a_{2}=4 )
( <a_{1},a_{2}> = <a_{2},a_{1}>+18 & a_{1}+a_{2}=8 ) <==> ( a_{1}=5 & a_{2}=3 )
( <a_{1},a_{2}> = <a_{2},a_{1}>+36 & a_{1}+a_{2}=8 ) <==> ( a_{1}=6 & a_{2}=2 )
( <a_{1},a_{2}> = <a_{2},a_{1}>+54 & a_{1}+a_{2}=8 ) <==> ( a_{1}=7 & a_{2}=1 )


( <a_{1},a_{2}> = <a_{2},a_{1}>+9 & a_{1}+a_{2}=7 ) <==> ( a_{1}=4 & a_{2}=3 )
( <a_{1},a_{2}> = <a_{2},a_{1}>+27 & a_{1}+a_{2}=7 ) <==> ( a_{1}=5 & a_{2}=2 )
( <a_{1},a_{2}> = <a_{2},a_{1}>+45 & a_{1}+a_{2}=7 ) <==> ( a_{1}=6 & a_{2}=1 )


( <a_{1},a_{2}> = <a_{2},a_{1}> & a_{1}+a_{2}=6 ) <==> ( a_{1}=3 & a_{2}=3 )
( <a_{1},a_{2}> = <a_{2},a_{1}>+18 & a_{1}+a_{2}=6 ) <==> ( a_{1}=4 & a_{2}=2 )
( <a_{1},a_{2}> = <a_{2},a_{1}>+36 & a_{1}+a_{2}=6 ) <==> ( a_{1}=5 & a_{2}=1 )


( <a_{1},a_{2}> = <a_{2},a_{1}>+9 & a_{1}+a_{2}=5 ) <==> ( a_{1}=3 & a_{2}=2 )
( <a_{1},a_{2}> = <a_{2},a_{1}>+27 & a_{1}+a_{2}=5 ) <==> ( a_{1}=4 & a_{2}=1 )


( <a_{1},a_{2}> = <a_{2},a_{1}> & a_{1}+a_{2}=4 ) <==> ( a_{1}=2 & a_{2}=2 )
( <a_{1},a_{2}> = <a_{2},a_{1}>+18 & a_{1}+a_{2}=4 ) <==> ( a_{1}=3 & a_{2}=1 )


( <a_{1},a_{2}> = <a_{2},a_{1}>+9 & a_{1}+a_{2}=3 ) <==> ( a_{1}=2 & a_{2}=1 )


( <a_{1},a_{2}> = <a_{2},a_{1}> & a_{1}+a_{2}=2 ) <==> ( a_{1}=1 & a_{2}=1 )


teorema:
<a_{1},a_{2}> = <a_{2},a_{1}>+(a_{1}+(-1)a_{2})·(10+(-1))
<a_{1},a_{2}> = <a_{2},a_{1}>+(a_{1}+(-1)a_{2})·9


teorema:
<a_{1},a_{2}> = <a_{2},a_{1}>+(2a_{1}+(-n))·9 & a_{1}+a_{2}=n

ecuacions diofàntiques enteres

x^{2}+y^{2}=z
[2k+1]^{2}+[(2i)·k]^{2}=[4k+1]


x^{2}+y^{2}=z^{2}
[3k]^{2}+[4k]^{2}=[5k]^{2}


x^{3}+y^{3}+z=s^{2}
[3k+1]^{3}+[3·e^{(pi/3)i}k]^{3}+[3k]=[9k^{2}+6k+1]=[3k+1]^{2}


x^{4}+( y^{2}+(-5)z^{2} )·[k]^{2}=[k]·s^{3}
[3k]^{4}+( [8k]^{2}+(-5)[2k]^{2} )·[k]^{2}=[125k^{4}]=[k]·[5k]^{3}


x^{4}+y^{4}+(-2)z^{2}+3=4s^{3}
[3k+1]^{4}+[3e^{(pi/4)i}k]^{4}+(-2)[3k]^{2}+3=4[27k^{3}+9k^{2}+3k+1]=4[3k+1]^{3}

testimoni de Déu fundacional de la universtat de Stroniken

teoría de construcción

El milagro en la construcción:
1o inductivos: ( Si pones uno ==> se ponen todos )  <==> [An][ f(n) ==> f(n+1) ].
2o duales: ( rompes uno <==> se arreglan todos )  <==> [ ¬[Ex][ ¬f(x) ] <==> [Ax][ f(x) ]  ]
Material próximo al lugar de obra.


El miracle en la construcció:
1r inductius: ( Si poses uno ==> es posen tots )  <==> [An][ f(n) ==> f(n+1) ].
2n duals: ( trenques un <==> se arreglen tots )  <==> [ ¬[Ex][ ¬f(x) ] <==> [Ax][ f(x) ]  ]
Material próxim al lloc d'obra.

italiano

presente
tomare un capuccino


pasato próximo
havere tomato un capuccino


pasato perifrástico
váreti tomare un capuccino


pasato imperfecto
tomáveti un capuccino


futuro
tomareti un capuccino


futuro composto
habreti tomato un capuccino


subjuntivo
tomáseti un capuccino


subjuntivo composto
hubiéseti tomato un capuccino


condicionale
tomaríeti un capuccino


condicionale composto
habríeti tomato un capuccino

ecuació diferencial de producte integral invers

d_{xx}^{2}[ f(g(x)) [o(x)o] g(x)^{[o(x)o](-1)} ]  = (x^{m_{1}}+...(n)...+x^{m_{n}})·f(g(x))


f(g(x)) = e^{g(x)}
g(x) = int[ x^{n_{1}}+...(n)...+x^{m_{n}} ]d[x]

solució de ecuacions diferencials en series

d_{xx}^{2}[f(x)]=x^{n}·f(x)


f(x) = ∑ ( 1/((n+2)k+(n+1))(n+2)k+(n+2))! )·x^{(n+2)(k+1)}


d_{xx}^{2}[f(x)] = ∑ ( 1/((n+2)(k+(-1))+(n+1))((n+2)(k+(-1))+(n+2))! )·x^{(n+2)k}·x^{n}
d_{xx}^{2}[f(x)] = ∑ ( 1/((n+2)p+(n+1))((n+2)p+(n+2))! )·x^{(n+2)(p+1)}·x^{n}
k+(-1)=p & k=p+1


d_{x,...,x}^{m}[f(x)]=x^{n}·f(x)


f(x) = ∑ ( 1/((n+m)k+(n+1))·...·(n+m)k+(n+m))! )·x^{(n+m)(k+1)}