# D. H. LEHMER PROBLEM OVER HALF INTERVALS

• Xu, Zhefeng
• Published : 2009.05.01
• 69 5

#### Abstract

Let $q\;{\geq}\;3$ be an odd integer and a be an integer coprime to q. Denote by N(a, q) the number of pairs of integers b, c with $bc\;{\equiv}\;a$ (mod q), $1\;{\leq}\;b$, $c\;{\leq}\;{\frac{q-1}{2}}$ and with b, c having different parity. The main purpose of this paper is to study the sum ${\sum}^{'q}_{a=1}\;$N(a,\;q)\;-\;\frac{{\phi}(q)}{8}$^2$ and obtain a sharp asymptotic formula.

#### Keywords

error term;mean value;asymptotic formula

#### References

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