SOME REMARKS ON A PAPER OF McCARTHY
نویسنده
چکیده
As usual we denote the number of integers not exceeding n and relatively prime to n by Euler's 0 function 0(n). Lehmer 2) calls the A (n) integers 1=a,< a 2 <. .. k. Lehmer) says that the totatives are uniformly distributed with respect to k. To shorten the notation we say that T(n, k) holds in this case. Lehmer 2) further calls n exceptional with respect to k if either n is divisible by k 2 or n has a prime factor of the form kx + 1. He shows that for all exceptional n, T(n, k) holds. In a recent note McCarthy1) proves that if k is a prime then T(n, k) holds if and only if n is exceptional with respect to k. However, if k is not squarefree there is an integer n > k which is not exceptional and for which T(n, k) holds. He further asks if the second half of his theorem remains true if k is not a prime but is squarefree. We are going to prove this in this note .
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