The remainder of 2^59!/255

Dear Student,
Please find below the solution to the asked query:

As, 2^{59} = 2^{3} \times 2^{56} = 2^{3} \times {(2^{8})}^{7} = 2^{3} \times {(256)}^{7} As, the remainder when 256 is divided by 255 = 1 \Rightarrow the remainder when 256^{7} is divided by 255 = 1^{7} = 1 \Rightarrow the remainder when 2^{59} is divided by 255 = 2^{3} \times 1 = 8

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