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 of without using a factorisation algorithm.
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.