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We classify the real and strongly real conjugacy classes in GL n( q) and SL n( q). In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes. This paper is the first of two that together classify the real and strongly real classes in GL n( q), SL n( q), PGL n( q), PSL n( q), and all quasi-simple covers of PSL n( q). [ABSTRACT FROM AUTHOR]

Let ΦΦ( x) be the number of the integers n such that φφ( n) ≤≤ x, where φφ denotes the Euler function. In this paper we give an explicit form of Bateman's theorem for the remainder term ΦΦ( x) -- Ax where A == ζζ(2) ζζ(3)/ ζζ(6). [ABSTRACT FROM AUTHOR]