Quadrat aus Produkt

from math import sqrt

a=[1,3,8,120]

for i in range(1,100000000):
    res = sqrt(3*(i**2-1)+1)
    if res%1==0:
        yes=True
        for j in a:
            res = sqrt(j*(i**2-1)+1)
            if res%1!=0:
                yes=False
        if yes:
            print(i**2-1)