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The well-known Carmichael conjecture concerns the set of positive\udintegers (presumed empty) which occur as a value of the Euler\udfunction at one positive integer but at no others. We study the\udanalogous problem for the Carmichael function. We also study the\ud(far more numerous) sets of integers which occur in the image of\udone of these functions but not of the other,\udas well as those which occur in the image of both

Coincidences in the values of the Euler and Carmichael functions