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 ...

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 ...