There are two little equations involving Euler's totient function which I'm not sure how to solve:

(a)Solve the equation .

(b)Given that is a product of two primes and that , find the Prime factorisation ofwithout using a factorisation algorithm.

Attempt:

For(a)I know that if then the totient function is given by . And if n has prime factorization , then it is given by:

So in this case we have

So, how should I work backward to find n?

For(b), since where p & q (the question doesn't say if they are distinct) are primes we'll have:

Now, how can I tell what p and q are without factorizing n?

Any guidance is greatly appreciated.