Sum of sum of sum?

Number Theory Level 3

Let A A be the sum of digits of 444 4 4444 4444^{4444} , and let B B be the sum of digits of A A . Find the sum of digits of B B .


The answer is 7.

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Gaurav Gupta by Gaurav Gupta , 28, India

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1 solution

Gaurav Gupta
Sep 11, 2016

First prove that sum of digits of B is less than 12 now 4444=7 mod 9 and 7^3=1mod 9 so 4444^4444=7 mod 9 so sum of digits of B is 7

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