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This article is cited in 11 scientific papers (total in 11 papers)
On the number of solutions of an $n$th degree congruence with one unknown
S. V. Konyagin
Abstract:
We show that the number of solutions to the congruence $f(x)\equiv 0\pmod m$, where $f(x)$ is a polynomial of degree $n\geqslant2$ whose coefficients have greatest common divisor relatively prime to $m$, does not exceed $(n/e+O(\ln^2 n))m^{1-1/n}$, where $n/e+O(\ln^2n)$ cannot be replaced by $n/e$.
Bibliography: 5 titles.
Received: 11.07.1978
Citation:
S. V. Konyagin, “On the number of solutions of an $n$th degree congruence with one unknown”, Mat. Sb. (N.S.), 109(151):2(6) (1979), 171–187; Math. USSR-Sb., 37:2 (1980), 151–166
Linking options:
https://www.mathnet.ru/eng/sm2363https://doi.org/10.1070/SM1980v037n02ABEH001947 https://www.mathnet.ru/eng/sm/v151/i2/p171
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Abstract page: | 722 | Russian version PDF: | 233 | English version PDF: | 17 | References: | 80 | First page: | 2 |
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