Choosing e and d in RSA I just finished watching a video explaining RSA where the following example was used:

Choose two random prime numbers:

$$P=2, Q=7$$

compute $n = pq$

$$2\times7 = 14$$

Compute the totient $\phi(n) = (p-1)(q-1)$

$$6\times 1 = 6$$

Choose $e$ that $e &gt; 1$ and coprime to $6$ 

$$e=5$$

choose $d$ to satisfy $de \equiv 1 \pmod {\phi (n)}$ 

$$5d \equiv 1 \pmod 6$$

The instructor then goes on to say d may have multiple solutions $5,11,17, \ldots$

but the example I read prior to the video indicated that d had a unique solution.  Please help.
It's a unique solution $\bmod 6$, but any value $5+6k$ is from the same equivalence class.
In general, take a prime number such as a fixed one like a Mersenne number or a prime using a primality test.