Carmichael's conjecture states that if φ (x) = n, then φ (y) = n for some y ≠ x (φ is Euler's totient function). We show that the conjecture is valid for all x under 10 10,900,000. The main new idea ...

Google celebrates the birthday of Leonhard Euler, a Swiss mathematician recognized for popularizing much of modern math terminology and notation, as well as famous contributions to calculus and ...

A stretch too far, perhaps, but Nahin’s tale of the formula ei π + 1 = 0, which links five of the most important numbers in mathematics, is remarkable.