Question

Find the remainder when 1021^1022 is divided by 1023?​

Answer 1

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1022 :: —2 (mod 1024)

=> 1022^10 :: (—2)^10 =1024:: 0 (mod 1024)

i.e. remainder when 1022^10 is divided by 1024, remainder is 0. Now, 1022^1023=1022^10*1022^1013. Hence the whole thing is divisible by 1024.

Hence the remainder is 0