abcde+ edcba=77777
10000a+1000b+100c+10d+e+10000e+1000d+100c+10b+a=77777
10001a+1010b+200c+1010d+10001e=77777
10001(a+e)+1010(b+d)+200c=77777
Deoarece u(1010(b+d))=0 si u(200c)=0 rezulta u(10001(a+e))=7=>
a+e=7
1010(b+d)+200c=77777-70007
1010(b+d)+200c=7770 |: 10
101(b+d)+20c=777
Deoarece u(20c)=0=> u(101(b+d))=7=> b+d=7
20c=777-707
20c=70 |:10
2c=7
c=7:2=3,5
Deoarece c nu este o cifra de la 0 la 9 , deducem ca nu exista numere naturale de forma data care insumate sa dea 77777.