Answer: 7744=88*88
It is easy as soon as you perceive that A+B=11
Remark:
clearly AABB is divisible by 11, hence by 121.
so A0B is also divisible by 11.
For any number to be divisible by 11 , one evaluates
two sums: SO - the sum of all the digits found on the odd-numbered places , and SE -the sum of all the digits found on the even-numbered places . The absolute value of SO-SE has to be divisible by 11.
Hence A+B=11.
There are only 2 possibilities for a square to be terminated by two identical digits ==> BB IS EITHER 00 or 44.
Hence the answer 7744=88^2
ady

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