Abstract
Let a, b, c be nonzero polynomials in k[t] where k[t] is the ring of polynomials with coefficients in k. We prove that if ax2+by2+cz2=0 has a nonzero solution in k[t], then there exist x, y, z∈ k[ t] , not all zero, such that ax02+by02+cz02=0 and degx0≤12(degb+degc), degy0≤12(dega+degc), and degz0≤12(dega+degb). This is the polynomial analogue of Holzer’s theorem for ax2+by2+cz2=0 when a, b, c are integers.
Original language | English |
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Pages (from-to) | 351-355 |
Number of pages | 5 |
Journal | Ramanujan Journal |
Volume | 48 |
Issue number | 2 |
DOIs | |
State | Published - Feb 15 2019 |
Bibliographical note
Publisher Copyright:© 2017, Springer Science+Business Media, LLC.
Keywords
- Holzer’s theorem
- Legendre equation
- Rational polynomial ring
ASJC Scopus subject areas
- Algebra and Number Theory