find the remainder when 4444的4444次方 is divided by 9
please steps by steps because i just learning it
4444^4444 = (494*9-2)^4444(494*9-2)^4444 ≣ 2^4444 (mod 9)2^4444=2*8^1481=2*(9-1)^14812*(9-1)^1481 ≣ 2*(-1) (mod 9)2*(-1) ≣7 (mod 9)Ans： 7
整數除以9的餘數即是數字和除以9的餘數
4444^4444(mod9)
=7^4444(mod9)
=(7^3)^1481*7(mod9)
=343^1481*7(mod9)
=1^1481*7(mod9)
=7
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4444^4444 = (494*9-2)^4444(494*9-2)^4444 ≣ 2^4444 (mod 9)2^4444=2*8^1481=2*(9-1)^14812*(9-1)^1481 ≣ 2*(-1) (mod 9)2*(-1) ≣7 (mod 9)Ans： 7
整數除以9的餘數即是數字和除以9的餘數
4444^4444(mod9)
=7^4444(mod9)
=(7^3)^1481*7(mod9)
=343^1481*7(mod9)
=1^1481*7(mod9)
=7