Suppose n is the product of two distinct odd primes p and q

Suppose n is the product of two distinct odd primes p and q. hollowing the steps below to show that factoring n is as hard as finding an integer a satisfying a^2 = 1 (mod n) and a plusminus 1 (mod n).

Solution

n is a product of two distinct odd primes p and q

for example 143=11*13

factors of 143 are 1,11,13 and 143

we do not find any other factor for product of two odd primes.

similarly it is hard to satisfy the conditions given in the question