(a,a)²=a,ba ⇔
(aa/10)²=a,ba ⇔
aa ²/100=aba/100 ⇔
aa ²=aba
Patratele perfecte de forma aba sunt
aba∈{121;484}
Consideram
aa ²=121 ⇔aa ²=11² ⇒aa=11 ⇒a=1;
aa ²=484 ⇔aa ²=22² ⇒aa=22 ⇒a=2;
A doua varianta nu convine deoarece aba=484 ⇒a=4 iar aa=22 ⇒a=2 ⇔4=2 ⇒fals;
In concluzie
ab=12
