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Grade 10Magical Mathematics[Interesting Approach]

when 4444^4444is written in decimal notation sum of its digit is 7 sum of digit is A sum of digits of A is B find sum of digitgs of B

AMAN MITTAL

8 Years agoGrade 10

1 Answer

Arun

8 Years ago

remainder by 9 = digit sum of sum of first 1002 natural numbers = 1002*1003/2 mod 9
=> 501*1003 mod 9 = 6*4 mod 9 = 24 mod 9 = 6 mod 9

=> 501*1003 mod 9 = 6*4 mod 9 = 24 mod 9 = 6 mod 9

when 4444^4444 is written in decimal notation,the sum of its digits is a. Let b be the sum of the digits of a. Find the sum of the digits of b

4444^4444 = 7^4444 mod (9) = 2^4444 mod (9) = (2^3)^1481 * 2 mod (9)
=> (2^3)^1481 * 2 mod (9) = 8^1481 * 2 mod (9) = -2 mod (9) = 7 mod 9

Regards

Arun (askIITiana forum expert)

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