Sum of digits NUMBER THEORY problem | Mathematics | Page 1

south cloud Dec 31, 2025, 5:28 AM

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What is the sum of the digits of 2^100?

Ik that the number must be congruent to 7 mod 9, but after that how would I proceed?

ornate idolBOT Dec 31, 2025, 5:28 AM

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pine venture Dec 31, 2025, 5:30 AM

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i was about to tell you the sum of digits if the number is written in binary lol

south cloud Dec 31, 2025, 5:33 AM

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yo why is there no number theory tag lol

pine venture Dec 31, 2025, 5:33 AM

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yeah just noticed

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maybe just write number theory in your title in capital letters that would grab attention

south cloud Dec 31, 2025, 5:37 AM

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Sum of digits NUMBER THEORY problem

graceful kindle Dec 31, 2025, 5:52 AM

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I would be very suprised if a 'formula' for computing this would exist (or that it is known). I think that generally, in number theory, connecting multiplication (taking 2 to the power 100) and how a number looks (its representation in base 10) are quite hard to connect.

I would just simply code this one out

pine venture Dec 31, 2025, 6:10 AM

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just check if we could do anything by using mod 10 as it might help you get the digits

plucky ether Dec 31, 2025, 10:12 AM

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I think you need to apply the theorem "n congruent to S(n) mod 9" so your sum is gonna be of form 7+ 9k or something idk

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Here S(n) is the sum of digits of n

river fable Dec 31, 2025, 11:49 AM

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i just ask AI and he said you cannot get exact number without calculating exactly what 2^100 is. idk AI wrong or maybe your question is wrong idk

hidden latch Dec 31, 2025, 12:50 PM

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I found a way for 2^98 lemme know if y'all wanna continue

plucky ether Dec 31, 2025, 6:05 PM

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hidden latch I found a way for 2^98 lemme know if y'all wanna continue

Can you explain how?? Please

south cloud Dec 31, 2025, 8:43 PM

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plucky ether I think you need to apply the theorem "n congruent to S(n) mod 9" so your sum is...

yeah thats what I was able to do until originally

#Sum of digits NUMBER THEORY problem