摘要
Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（m） In this paper, we obtain the asymptotic formula： .G（x）=αx^2＋O（xlogx）,ax x→∞ Our result improves the corresponding result with an error term O（xlog^2 x） of Yang Zhaohua obtained in 1986
Let m be a positive integer, g(m) be the number of integers t for which 1≤t≤m and there does not exist a positive integer n satisfying (t=t(n))t~ n+1 ≡t(modm).For a number x≥3, letG(x)=∑m≤xg(m).In this paper, we obtain the asymptotic formula:G(x)=αx^2+O(xlogx),as x→∞. Our result improves the corresponding result with an error term O(xlog^2x) of Yang Zhaohua obtained in 1986.
