On the Equation n_1n_2= n_3n_4 Restricted to Factor Closed Sets |
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| Authors: | San Ying SHI Michel WEBER |
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| Affiliation: | 1. School of Mathematics, Hefei University of Technology, Hefei 230009, P. R. China;2. IRMA, UMR 7501, 7 rue René Descartes, 67084 Strasbourg Cedex, France |
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| Abstract: | We study the number of solutions N(B, F) of the diophantine equation n1n2=n3n4, where 1 ≤ n1 ≤ B, 1 ≤ n3 ≤ B, n2, n4 ∈ F and F⊂[1, B] is a factor closed set. We study more particularly the case when F={m=p1ε1…pkεk, εj ∈ {0, 1}, 1 ≤ j ≤ k}, p1,…, pk being distinct prime numbers. |
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| Keywords: | Diophantine equation arithmetical functions factor closed set |
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