Several Special Kinds of Indeterminate Equations Study 

Author  GaoZuoZuo 
Tutor  GuoJinBao 
School  Yan'an University 
Course  Basic mathematics 
Keywords  Indeterminate equation Integer solution Congruence Recursive sequences Algebraic Number Theory 
CLC  O156.1 
Type  Master's thesis 
Year  2010 
Downloads  155 
Quotes  0 
Diophantine equation Diophantine equations known , is a very important number theory research , which results not only on the development of various branches of mathematics plays an important role , but also for other nonmathematical disciplines ( such as physics , economics ) research have significant application value , therefore, is one of many mathematical indefinite equation has been the object of research workers enthusiastic . indefinite equation is an ancient Diophantine problem, apply elementary methods to solve more difficult ; many ways seem simple , but it is not easy to think of . this elementary and higher utilization methods, several special class of indefinite equation integer solution issues. mainly includes the following three aspects: 1 . introduces indefinite equation x3 ± 1 = Dyn research progress, and use recursive sequences , congruence theory proved diophantine equation x31 = 65y2 only integer solution (x, y) = (1,0) .2. introduced indefinite equation x3 ± B = Dyn Recent development and use algebraic number theory to study the uncertain equation x3 13 = y2 situation .3 integer solution is introduced indefinite equation Ax2 B = Cyn Recent development and utilization of elementary number theory and algebraic number theory to study the indefinite equation x2 4 = y5, x2 64 = y5 and x2 64 = y7 integer solution conditions .