RSA Algorithm Question

Question

• Suppose the primes p and q used in the RSA algorithm are consecutive primes (meaning they differ by 2). How would you factor n = pq?

• The ciphertext 10787770728 was encrypted using n = 10993522499 and e = 113. The factors p and q of n were chosen so that p - q = 2. Use your method in part (a) to decrypt the message

Answer 1

Set $n^2-1=10993522499$.
Isolate $n^2$.
$n$ is its positive square root.
Your two factors are $n-1$ and $n+1$.