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Jumbo Digits (Posted on 2013-06-14) Difficulty: 2 of 5
Find last three digits of the number

201920202021

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution No Subject Comment 1 of 1

2020 is a multiple of 10 and 2020^2021 ends with 2021 zeros, and therefore is a multiple of 50.

2019^50 =
 1806408412805678530166132731341369433406520546733673889642822689066841933346897
94470936642084400304647484512490891664968113712908110682601629876467326313340661
7589001

which ends in 001. Any power of this ends in 001.

The answer is 001.

In fact the last many many digits are a long string of zeros and a 1 at the end.


  Posted by Charlie on 2013-06-14 12:53:06
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