This number is its own cube

The cube of 51 is ending in 51, the cube of 249 is ending in 249 etc...

How many 30 digit numbers whose cube is ending by the same number ?
Solution

As a pocket calculator able to get the cube of so big numbers is unavailable, I give you a hint :
The square of A = 893380022607743740081787109376 is ending by A.
Deduce from that every 30 digit numbers whose cube ends in themselves.
Solution

Details

 

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