Question

(2+1)(2^2+1)(2^4+1)(2^8+1)/(2^8-1) = 4^n+1, then n is
(1)4
(2) 3
(3) 2
(4) 1​

Answer 1

Answer:

$(2 + 1)( {2 }^{2} + 1)( {2}^{4} + 1)( {2}^{8} + 1)( {2}^{8} - 1) = {4}^{n} + 1 \\ (3)(5)(17)(65)(63) = {4}^{n} + 1 \\ 1044225 = {4}^{n} + 1 \\ \\ 1044225 - 1 = {4}^{n} \\ 1044224 = {4}^{n}$

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