| The distribution of integer has important significance in elementary number theory, many experts and scholars have studied it. For example, Zhang Wenpeng studied the mean value of the distribution of integer and its inverse, Xu Zhefeng studied the mean value of an integer and its m-th power mod n over incomplete intervals. This paper uses many classical result and elementary skills to study the relevant mean value of the integer power and generalized D.H. Lehmer number. Specifically I studied the following two content:1.Set p for odd prime,k for non negative integers. Let (am)p represent the integer that meet 1≤ b≤ p and am≡ b(mod p). When the positive integer l,m meet l(?) m(mod (p - 1)), I studied the mean value of the formula And give the asymptotic formula.2.Set λ be any real number that meets λ ∈ (0,1], Order n> [1/λ]is odd prime and m≥ 2 is an integer, then for the arbitrary non negative integer k. When the integer ais the generalized D.H.Lehmer number, I studied the mean value of and give the asymptotic formula. |
