prime numbers

I had given a problem based on this application....

but no one ever solved it :P :D

This is by unique factorization theorem..

that every number can be represented as the product of primes in only one way..

THe LHS has every term as a unique factor.. i mean no two terms on the LHS are the same..

WHIle RHS has all the numbers in their reciprocal form..

Now think

karna.. the idea is fairly simple

For any number on the left (1/r) there is a unique multiplication that will exist (the product of the reciprocal of the powers of its prime factors)

And for every number on the right there will be unique number of the form 1/n

These two follow from unique factorization theorem.