This analysis reveals integer solutions for the Jin-Schmidt equation using Lucas numbers, suggesting connections to number theory.
In this paper, we study the integer solutions of the following equation that is so called the Jin-Schmidt equation, AX2+BY2+CZ2=DXYZ+1, where (X,Y,Z)=(Li,Lj,Lk), with i,j,k≥1 such that Li, Lj and Lk represent terms in the Lucas sequence that is defined by the relation L0=2, L1=1, Ln+1=Ln+Ln−1 with n≥1.
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Alabrahimi et al. (2025) studied this question.
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