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What would be the sum of the digits of 4444^4444?

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What would be the sum of the digits of 4444^4444?
posted Apr 22, 2017 by anonymous

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1 Answer

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Any numbers mod 9 value gives us the recursive sum of its digits for ex: 112 = 1+1+2 = 4 is the sum of digits
112 mod 9 = 4 mod 9 = 4 is the sum of digits
Similarly

4444 = 7 mod 9
4444^(4444) = 7^(4444) mod 9
4444^(4444) = 7*7^(3)(1481) mod 9
Since 7^3 mod 9 = 1 mod 9
7*7^(3)(1481) mod 9 = 7*(1)^1481 mod 9 = 7 mod 9
ie., 4444^(4444) = 7 mod 9 ===> 7 is the recursive sum of its digits.

answer Apr 23, 2017 by Tejas Naik



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