For decades, a math puzzle has stumped the smartest mathematicians in the world. x 3 +y 3 +z 3 =k, with k being all the numbers from one to 100, is a Diophantine equation that's sometimes known as ...

We derive midpoint criteria for solving Pell's equation x² - Dy² = ±1, using the nearest square continued fraction expansion of $\sqrt D $ . The period of the expansion is on average 70% that of the ...