mersenneforum.org - View Single Post - Closed form solution of x^2 = 2 mod Fermat number

alpertron · 2005-08-18, 16:47

Using n=5, F₅ = 4294967297.

With your method you find sqrt(2) = 4278190337.

If you somehow find sqrt(2) = 1370209359, you will be able to factor F₅ since gcd(F₅, 4278190337 - 1370209359) = 6700417 which is a proper factor of the original number.

2005-08-18, 16:47	#6
alpertron Aug 2002 Buenos Aires, Argentina 3²×149 Posts	Using n=5, F₅ = 4294967297. With your method you find sqrt(2) = 4278190337. If you somehow find sqrt(2) = 1370209359, you will be able to factor F₅ since gcd(F₅, 4278190337 - 1370209359) = 6700417 which is a proper factor of the original number.