关于不定方程x^3-1=181y^2
On the diophantine equation x^3-1=181y^2
云南民族大学学报:自然科学版,2017,26(1):38-40

樊苗 FM

摘要


设p为素数且p≡1(mod6).关于不定方程x^3-1=py^2的求解是数论的重要研究课题之一.研究p=181时不定方程x^3-1=py^2的可解性问题. 利用递归数列,同余式,Pell方程解的性质证明了不定方程x^3-1=181y^2仅有整数解(x,y)=(1,0). Let be a prime with p≡1(mod 6). Solving the diophantine equation x^3-1=py^2 is one of the important topics in the number theory. The solvability of the diophantine equation x^3-1=py^2 with p=181 is investigated. By using the recurrent sequence, congruence and some properties of the solutions to Pell equation, it is proved that the diophantine equation x^3-1=py^2 has only integer solution (x,y)=(1,0).

参考



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