Dissertation > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Number Theory > Elementary Number Theory

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
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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 .

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