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Based on this problem.

Define two positive integer sequences \(\{a_n\}\) and \(\{b_n\}\) be defined as \(a_1\ne b_1\), \(a_{n+1}=a_n+k\) and \(b_{n+1}=b_n+k\). These ...

\[\int_0^{\frac{\sqrt{2} }{2} } \frac{\arcsin x}{x} dx = \frac{a}{b}G +\frac{c}{d}\pi^k \ln(m),\]

where \(a,b,c,d,k,m\) are positive ...

Find the sum of all distinct \(a \in \mathbb{N}\) for which there exists a positive integer \(b\) such that ...

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