There exists a number oddity with three different 4-digit duodecimal (base 12) positive integers. One is BA01, where: (BA+01)2= BA01.
It also works with 3630 as: (36+30)2 = 3630
What is the other number?
What is the smallest 6-digit duodecimal positive integer that would work?
(in other words, in a 6-digit number pqrstu with pqrstu=(pqr+stu)2, where each of the letters denote a base 12 digit whether same or different.)
Note: None of the numbers can contain leading zeroes.