Fermat

enc = 19680371928191389865779839985791596167665873169713320020521150351814544808795290799819143739285034284618916611967016738463398067633445648709977850622867289722372596963247707263439220754822048132943713516661678425983400991090507601151379737471045664186065701334581916822015055797618213572309286829285344833292619972478164124966
e = 968652731
n = 102540217756563657047332566955337115791446221732625727452582331508051620795222012389711690721710744258138643196665107838857343318370676047259451056400766716545743614936642796054577351416225937660442147520898979450408123775720780029305387983864387834538862252970711456364395296680415434192049384435099401099371935534988486952679

def fermat(n,k):
    bits=(len(bin(n))-2)
    bits=bits//2+bits%2

    l=bits-k

    #4 value of a is narrowwed down to a1, a2
    a1=2^(k-2)+2^(l-2)-10^4
    a2=-2^(k-2)+2^(l-2)-10^4

    while 1:
        if is_square(a1^2+n):
            print sqrt(n+a1^2)+a1
            break
        if is_square(a2^2+n):
            print sqrt(n+a2^2)+a2
            break
        a1+=1
        a2+=1

class Timeout():
    """Timeout class using ALARM signal."""
    class Timeout(Exception):
        pass

    def __init__(self, sec):
        self.sec = sec

    def __enter__(self):
        signal.signal(signal.SIGALRM, self.raise_timeout)
        signal.alarm(self.sec)

    def __exit__(self, *args):
        signal.alarm(0)    # disable alarm

    def raise_timeout(self, *args):
        raise Timeout.Timeout()


for i in range(256,1,-1):
    try:
        with Timeout(3):
            fermat(n,i)
    except:
        pass