On the number of solutions of Znám's problem (Q2742288)
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scientific article; zbMATH DE number 1649846
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of solutions of Znám's problem |
scientific article; zbMATH DE number 1649846 |
Statements
20 September 2001
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Znám problem
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system of congruences
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On the number of solutions of Znám's problem (English)
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For any positive integer \(s\) with \(s>1\), let \(Z(s)\) denote the number of positive integer solutions \((x_1,x_2,\cdots,x_s)\) of the system of congruences \(x_1x_2\cdots x_s/x_i+1\equiv 0\pmod{x_i} (i=1,2,\cdots,s)\) with \(1<x_1<x_2<\cdots<x_s\). In this paper the authors prove that if \(s\geq 12\), then \(Z(s)\geq 39\).
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