Then . Plugging this back into the two equations and dividing, we have so that we have . Now we know that so that we have and that is a contradiction since product of two consecutive integers cannot be a perfect square.
Tapos . Plugging ito pabalik sa ang dalawang equation at naghahati, mayroon kaming kaya na kami . Ngayon ay alam namin na kaya na kami at iyon ay isang pagsalungat mula sa produkto ng dalawang magkakasunod na integers ay hindi maaaring isang perpektong parisukat.