# Number algebra calculus theory

**Number Theory**Level pending

A four digit number \(\overline{ABCA}\) fits into the following equations

\[\overline{ABCA} + 10( \overline{AA} - \overline{BC}) = 5555\]

\[\overline{ABCA} - \overline{ACBA} = -90\]

\[C = A - B\]

Let \(n = A^2 - B^2 + C^2 - A^2\)

If

\[f_1(x) = \sqrt{x^3 + 3x^2 + 3x - 19}\]

and

\[f_2(\sqrt[3]{x} - 10) = \frac{42x}{54}\]

Find the largest prime divisor of \(\overline{ABCA} - (f_1(n) + f_2(n))\)

Details and assumptions

- \(\overline{ABCA} = 1000A + 100B + 10C + A\)