On the integer solutions of Diophantine equations x2－22y2＝1 and y2－Dz2＝1764
MA Huiyu1， QU Yunyun1,2， ZHANG Xue1
1.School of Mathematical Sciences， Guizhou Normal University， Guiyang 550001， China；2.School of Mathematical Sciences， Xiamen University， Xiamen 361005， China
Abstract：By using the method of recursive sequence and some properties of the solutions to Pell equation，the following conclusions are proved about the system of Diophantine equations x2－22y2＝1 and y2－Dz2＝1764：if D＝2p1…ps， 1≤s≤4 (p1，…，ps are distinct odd primes)， then(i)it has only trivial solution ＝ with the exception that D＝2×77617；(ii)it has integer solutions ＝， where D＝2×77617； if D＝pm(m∈Z＋，p is any prime)， it has only trivial solution ＝.
马慧宇,瞿云云,张 雪. 关于不定方程组x2－22y2＝1与y2－Dz2＝1764的公解[J]. 华中师范大学学报(自然科学版), 2018, 52(5): 613-618.
MA Huiyu,QU Yunyun,ZHANG Xue. On the integer solutions of Diophantine equations x2－22y2＝1 and y2－Dz2＝1764. journal1, 2018, 52(5): 613-618.
2018, Vol. 52 
