A number theory problem by Lakshya Bhatnagar
Number Theory
Level
2
Find the number of perfect cubes between 1 and 1000009 which are exactly divisible by 9.
The answer is 33.
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1 solution
Divisible by 9 means it should contain 3²..
All multiples of 3 when cubed will contain 3²
And 1000009 means maximum 100³
Hence multiples of 3 from 1-99 which is 33 (Ans)