On the Euler function of the Catalan numbers
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We study the solutions of the equation 0(Cm)/0(Cmn) = r, where r is a fixed rational number, Ck is the kth Catalan number and o is the Euler funcition. We note that the number r - 4 is special for this problem and for it we construct solutions (m, n) to the above equation which are related to primes p such that 2p - 1 or 4p - 3 is also prime.
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