I did how $256=-1$ mod $257$ and $2^8=256$ then $(2^8)^{15}=-1 $ mod $257$ and i conclude that $2^{125} \bmod 257 = 225$
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5Yes ${}{}{}{}{}{}{}$ – Some Guy Feb 23 '21 at 21:01
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1+1 Nice analysis, you nailed it. Further, it seems clear that your analysis, which focused on the relationship between $2^8$ and $(257)$ represents the intent of the problem composer. – user2661923 Feb 23 '21 at 21:05
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Who me? ${}{}{}{}{}$ – Some Guy Feb 23 '21 at 21:06
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1@SomeGuy I don't know who upvoted your comment. I was responding to the original poster, whose query I upvoted. – user2661923 Feb 23 '21 at 21:07