faster brute forcing

p=1033 #your lower factor
q=108271
n = p*q

i = 2
val = 2
while n%val != 0:
  qr = (n - (((9**(i))*2)%n))+2
  m = qr
  val = ((n/((((n+m)/(n-m))**0.5)-1))**0.5) + (((i-(((n/((((n+m)/(n-m))**0.5)-1))**0.5)/2))*2)+1)
  print(f"i: {i}, val: {val}")
  if n%val == 0:
    print("found p and q!")
    break
  i = i + 1

#I also have a version that may work for (p||q)/30