Question

Let a and b be positive integers such that the product of all positive divisors of a equals the product of all positive divisors of b. Prove that a

Answer 1

The property A*B = (A' + A") * ( B'+B") is equal to each other.

According to the statement

We have given that the a and b is the positive integers and we have to prove that the product of all positive divisors of a equals the product of all positive divisors of b.

And in this statement

Now we use Distributive property

Here A and B is the positive integer and

A' and A" are the divisors of A and B' and B" are the divisors of B.

Now,

A = A' + A" and B = B'+B"

Now, Multiply both with each other then

A*B = (A' + A") * ( B'+B")

then

A*B = (A' B'+ A'B") + ( A"B'+A'B")

by this way it is equal to each other

Hence proved.

So, The property A*B = (A' + A") * ( B'+B") is equal to each other.

Learn more about the Property here brainly.com/question/2807928

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