3
votes
3answers
885 views

Does knowing the totient of a number help factoring it?

Edit: The quoted question addresses only numbers of the form $p^a q^b$, I asked a general question for arbitrary $n$. If $n$ is a prime or a product of 2 primes then knowing its totient ...
2
votes
0answers
153 views

How many co-primes are there for a big integer N over a specified interval?

How many co-primes are there for a big integer $N$ over a specified interval ? bounds of $N$ are $[1,10^9]$ and the interval is $[a,b]$ where ($1\leq a\leq b \leq 10 ^{15}$) and there are $100$ ...
2
votes
1answer
413 views

Factoring a number $p^a q^b$ knowing its totient

We are given: $n=p^aq^b$ and $\phi(n)$, where $p,q$ are prime numbers. I have to calculate the $a,b,p,q$, possibly using computer for some calculations, but the method is supposed to be symbolically ...