Suppose you know n = 1141367 is a product of two primes. A cryptographer is
able to tell you that = 1136856. Find the two prime factors of n.
$\displaystyle \varphi (n) = \varphi (p_{1} \cdot p_{2}) = \varphi(p_{1}) \cdot \varphi (p_{2}) = (p_{1} - 1)(p_{2} - 1)$
So: $\displaystyle (p_{1} - 1)(p_{2} - 1) = 1136856$
But since: $\displaystyle n = p_{1}p_{2} \ \Rightarrow \ p_{2} = \frac{n}{p_{1}}$
We have that: $\displaystyle (p_{1}-1)\left(\frac{n}{p_{1}} - 1\right) = 1136856$
Should be easy from here.
AH beaten