Leonhard Euler, one of the greatest mathematicians of all time, was born 300 years ago on April 15, 1707.

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 ...

THOMAS J. OSLER, 92.43 Euler's little summation formula and special values of the zeta function, The Mathematical Gazette, Vol. 92, No. 524 (July 2008), pp. 295-299 ...