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