Perfect square and perfect cube
Number Theory
Level
4
What is the sum of all 7-digit numbers that are both a perfect square and a perfect cube?
The answer is 18113890.
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1 solution
For a number to be both a perfect square and a perfect cube it needs to be in a form of k 6 where k is an integer.
k 6 = ( k 3 ) 2 = ( k 2 ) 3
The list of k values that satisfy the conditions given are: 1 0 , 1 1 , 1 2 , 1 3 , 1 4 therefore the sum of k 6 is 18113890.