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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) )tn+1 ≡ t(modm).For a number x ≥ 3, letG(x) = ∑m≤xg(m).In this paper, we obtain the asymptotic formula:G(x) = αx2 + O(xlogx),as x→∞.Our result improves the corresponding result with an error term O(xlog2x) of Yang Zhaohua obtained in 1986.