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For how many integers from 1 to 100, inclusive, is x^3 - x^2  a perfect square?

 Oct 29, 2019
 #1
avatar+106539 
+1

Here's my attempt

 

x^3 -  x^2  =

 

x^2 * (x - 1)

 

We will have a perfect square whenever  (x - 1)  is a perfect square......so.....

 

x  = 1, 2,  5, 10, 17, 26, 37, 50, 65, 82

 

 

cool cool cool

 Oct 29, 2019

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