On the special values of the Riemann zeta-function (Q2741653)

For \(n\) be a positive integer, the author proves: There exist integers \(A'_n\), \(B'_n\) and \(C'_n\) such that NEWLINE\[NEWLINE0<A'_n+B'_n\zeta(3)+C'_n\zeta(4)<3\zeta(4)C^n_2NEWLINE\]NEWLINE, where \(C_2=3^4/89<1\). There exist integers \(A''_n\), \(B''_n\), \(C''_n\) and \(D'_n\) such that NEWLINE\[NEWLINE0<A''_n+B''_n\zeta(3)+C''_n\zeta(4)+D''_n\zeta(5)<4\zeta(5)C^n_3NEWLINE\]NEWLINE, where \(C_3=3^5/346<1\).