| Autor: | Zoltán Daróczy, Gabriella Hajdu |
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| Rok vydání: | 1999 |
| Předmět: | |
| Zdroj: | Acta Mathematica Hungarica. 82:1-9 |
| ISSN: | 0236-5294 |
| Popis: | In this paper our aim is to determine all the solutions of the functional equation f(a + b + c) + f(b + c + d) + f(a - d) = f(a + b + d) + f(a + c + d) + f(b - c), where a, b, c, d ∈ Zsatisfy ad = bc. This equation is a generalization of one of the identities of Ramanujan. He found two solutions, f(x) = x2, and f(x) = x4. We prove that every solution of the equation can be written as a linear combination of 11 independent solutions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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