Determine if the following problem is symmetric and transitive (1 Viewer)

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1. The problem statement, all variables and given/known data

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

2. Relevant equations
ab2 must ba2


3. 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?
 

tiny-tim

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Welcome to PF!

Hi Meager! Welcome to PF! :smile:
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:
 

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