Indicating with p and q the two prime factors of we have that...
... and that leads us to write the 'twin equations'...
... that are equivalent to second degree equation...
... the solutions of which are and ...
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.