Răspuns :
ab + bc + ca 10 a + b + 10 b + c + 10 c + a 11 a + 11 b + 11 c
----------------- = ----------------------------------------- = ------------------------ =
ac + cb + ba 10 a + c + 10 c + b + 10 b + a 11 a + 11 b + 11 c
11 × ( a + b + c ) a + b + c
= ----------------------- = --------------- → fractie echiunitara
11 × ( a + b + c ) a + b + c
----------------- = ----------------------------------------- = ------------------------ =
ac + cb + ba 10 a + c + 10 c + b + 10 b + a 11 a + 11 b + 11 c
11 × ( a + b + c ) a + b + c
= ----------------------- = --------------- → fractie echiunitara
11 × ( a + b + c ) a + b + c
10a+b+10b+c+10c+a=11a+11b+11c=11(a+b+c)
10a+c+10c+b+10b+a=11a+11c+11b=11(a+b+c)
11(a+b+c)/11(a+b+c)=1, C.C.T.D.
10a+c+10c+b+10b+a=11a+11c+11b=11(a+b+c)
11(a+b+c)/11(a+b+c)=1, C.C.T.D.