Math Help - Using sqrt(d) factor large number

If QQ' = N,is the large number you need to Factor . P is a parameter .then calculate d = P^2 + N .And using PQa algorithm expand Sqrt(d) .when arise P only itself .we can factor N .If we need to factor 247 .let P=8 . d=247 + 8^2=311 .then expand Sqrt(311) .next we can find what . The below is its process. [code] 311 a0=17 22a_1-17=5 a1=1
13a_2-5=8 a2=1
19a_3-8=11 a3=1 [/code ] We can find 247=13*19 .the key of the method is that ensure the P belonged d. Not expand P must bigger than (Q-Q')/2(via some formula) Im a chinese .Im learning English