The congruence equation a¯ + b¯ ≡c¯(modp)
Keyword(s):
In this paper, we consider the congruence equation [Formula: see text] with [Formula: see text] where [Formula: see text] denotes the multiplicative inverse of [Formula: see text]. We prove that its number of solutions is asymptotic to [Formula: see text] when [Formula: see text] by estimating a certain average of Kloosterman sums via Gauss sums. On the other hand, when [Formula: see text], the number of solutions has order of magnitude at least [Formula: see text]. It would be interesting to better understand its transition of behavior. By transforming the question slightly, one can relate the problem to a certain first moment of Dirichlet [Formula: see text]-functions at [Formula: see text].
1994 ◽
Vol 59
(6)
◽
pp. 1439-1450
◽
Keyword(s):
1968 ◽
Vol 11
(4)
◽
pp. 527-531
◽
Keyword(s):
Keyword(s):
1988 ◽
Vol 106
(5)
◽
pp. 1539-1543
◽
Keyword(s):
2020 ◽
pp. 111-134
Keyword(s):
2020 ◽
Vol 54
(2 (252))
◽
pp. 112-117
Keyword(s):