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Find the last three digits of 17^256

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@Shekhar

Solution: We have 172 Now, 17256 2 128 = (17 ) 289 = (290 - 1)128 -290 - (128) (290) +1 128C 2 126(290) 12SC127(290) + 1 , where m is a positive integer. = 1000 m + (128) (290) [(127) (145) - 1] + 1 = 1000 m + (128) (290) (18414) + 1 = 1000 Cm + 683527] + 680 + 1 = 1000 [m + 683527] + 681 Thus, the last three digits of 17256 are 681
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Pankaj

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