Let $a$ and $b$ be positive integers.

The extended Euclidean algorithm is an efficient way to find integers $u,v$ such that

$a \cdot u + b \cdot v = \gcd(a,b)$

Later, when we learn to decrypt RSA ciphertexts, we will need this algorithm to calculate the modular inverse of the public exponent.

Using the two primes $p = 26513, q = 32321$, find the integers $u,v$ such that

$p \cdot u + q \cdot v = \gcd(p,q)$

Enter whichever of $u$ and $v$ is the lower number as the flag.

Knowing that $p,q$ are prime, what would you expect $\gcd(p,q)$ to be? For more details on the extended Euclidean algorithm, check out this page.