Solving some parametric quadratic Diophantine equation over Z and Fp
Let t⩾ 2 be an integer. In this work, we consider the integer solutions to the Diophantine
equation D: x2+ (t− t2) y2+ (4− 8t) x+ (8t2− 8t) y+ 3= 0 over Z and over finite fields Fp for
primes p⩾ 2, respectively. We also derive some algebraic identities related to the integer
solutions of D including recurrence relations and continued fractions.
equation D: x2+ (t− t2) y2+ (4− 8t) x+ (8t2− 8t) y+ 3= 0 over Z and over finite fields Fp for
primes p⩾ 2, respectively. We also derive some algebraic identities related to the integer
solutions of D including recurrence relations and continued fractions.
Let t⩾2 be an integer. In this work, we consider the integer solutions to the Diophantine equation D: x2+(t−t2)y2+(4−8t)x+(8t2−8t)y+3=0 over Z and over finite fields Fp for primes p⩾2, respectively. We also derive some algebraic identities related to the integer solutions of D including recurrence relations and continued fractions.
Elsevier
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