Numbers...without numbers?

Number Theory Level 3

Consider a positive four digit number, \(\overline{ABCD}\).


\(A + B + C + D = \overline{AD}\)

C - B = A

\(\overline{AD} \times \overline{ DA} = \overline{ABCD}\)

What is number \(\overline{ABCD}\) in its numerical representation?

Details and assumptions. Each letter represents one numerical digit. ABCD is positive. AD is equivalent to 10A +D, not AxD.


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