Breaking RSA code

Question

I will be grateful for some tips on how to bite a task like so: I need to break a RSA code. I know that public key is $n=462257, e=13$. I also have cryptogram $c=139552$. The goal is to find a number that is encrypted here. I have written some things on wikipedia about RSA, but I am brand new on this area and I don't know how to even start. What is $c$ for in this task? What steps should I take to find the answer?

Answer 1

Start by factoring $n = 462257 = 503 \cdot 919 $. You can calculate $\varphi(n)$ and $d$ now since you know that $d \equiv e^{-1} \pmod{\varphi(n)}$. Given $d$, you can decrypt $m$ as usual. Alternatively, use the method suggested by Barry Cipra in the comments (brute force $m^{13} \equiv 139552 \pmod{462257}$).

You should get $m = 4242$.