Several Special Kinds of Indeterminate Equations Study
|Keywords||Indeterminate equation Integer solution Congruence Recursive sequences Algebraic Number Theory|
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 non-mathematical 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 x3-1 = 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 .