Determine if the following problem is symmetric and transitive

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Homework Statement



Suppose ~ is defined on the whole numbers by a~b iff ab2 is a perfect cube. Determine if ~ is
symmetric
transitive

Homework Equations


ab2 must ba2


The Attempt at a Solution



I tried using different numbers, but it isn't coming out as a perfect square.

For example, I said a=1
b=0........ Then this works.
Using other numbers it fails.

Should a=b?
 
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Welcome to PF!

Hi Meager! Welcome to PF! :smile:
Meager said:
Suppose ~ is defined on the whole numbers by a~b iff ab2 is a perfect cube. Determine if ~ is
symmetric
transitive

Hint: write a and b as a product of their prime factors. :wink:
 

Thread 'Finding the nth roots of a complex number'

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