Continuity Problem

Calculus Level 3

Let $$f(x)$$ be a piecewise function such that: \large f(x) = \begin{cases} \begin{align} & \cfrac{x^{2^{32}} - (4^{16})x + 4^{16} - 1}{(x - 1)^2} & , \hspace{1cm} x \ne 1 \\ & k & , \hspace{1cm} x = 1 \end{align} \end{cases}

Let $$k = a^b \times (a^c - 1)$$, where the value of $$k$$ make $$f(x)$$ continuous at 1.

If $$a$$ is a prime number and $$b < c$$ , solve for $$a + b + c$$ .

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