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Number Theory
Level
3
What are the last 10 digits of ?
Bonus: Can you generalize and prove it?
The answer is 5000033333.
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1 solution
Wow! The entire number is 1 6 6 6 6 5 0 0 0 0 3 3 3 3 3 , how surprising... so the last 10 digits are 5 0 0 0 0 3 3 3 3 3 .
I'm not sure why this occurs and would love to know. Does anyone have a great solution? I'm guessing it has something to do with the fact that x + y + z = 1 0 0 0 0 0 − 1 and maybe the factorization x 3 + y 3 + z 3 = ( x + y + z ) ( x 2 + y 2 + z 2 − x y − y z − z x ) + 3 x y z .