$5*13*97$ are factors of an expression in the question below. Factoring of the expression by 5, 13 and 97 which are prime factors should help identify a correct answer.

It's known that $3+2=5$, $3^2+2^2=13$ and $3^4+2^4=97$. IMO, the answer must be in the form of $3^n-2^n$ with $n$ defined as even number.

Answer choice C is matching $3^n-2^n$ format, as $3^{128} - 2^{128}$=$(3^{64} - 2^{64})(3^{64} + 2^{64})$=$(3^{32} - 2^{32})(3^{32} + 2^{32})(3^{64} - 2^{64})$ ... $...(3-2)$, where the last differential value is equal to 1

Answer is C