Let (a,b)=1 and ab=c^2. Show that a and b are perfect squares.

[nikolany]

hi all

I need some help with this question

Let (a,b)=1 and ab=c^2. Show that a and b are perfect squares.

Thank you

 

[Dick]

Look at the prime factorization of a, b and c.

 

[Mark44]

It took me a little while to comprehend what you meant by (a, b) = 1, but I concluded that you mean that a and b are relatively prime, namely that the largest factor they both share is 1.

To get you thinking about this the right way, try a few examples by assigning different values to a and b to see how that affects their products. The values you choose for a and b should be relatively prime. Keep in mind that your examples won't constitute a proof; they just help you think about the problem, and might help you formulate a real proof.