Integer Solutions Of Several Class Of Diophantine Equations

As an important branch of number theory, the indeterminate equation has comprehensive content and correlates closely to algebraic number the-ory, algebraic geometry and other parts of math. Some conclusion about the indeterminate equation are applied to Diophantine approximation, algebraic ge-ometry, p-adic and other relevant subjects. the research on the indeterminate equation have enriched the content of number theory widely.Although many scholars have research on the indeterminate equations, there is still a large research space on these problems.so that this thesis uses elemen-tary methods in theory of numbers to discuss and analyze several kinds of the indeterminate equation (equations) and reaches conclusions specifically:1. Some sufficient conditions are obtained that the indeterminate equations has no positive integer solution,where p is odd prime.2. Some sufficient conditions are obtained that the indeterminate equations has no positive integer solution,where p is odd prime.3. Some sufficient conditions are obtained that the indeterminate equation x3±1=py2 has no positive integer solution,where p is odd prime. And get countless p, where p is an odd prime of the form 6k+1, meet the equation x3±1=py2 without positive integer solution.4. A sufficient conditions is obtained that the indeterminate equations has no positive integer solution,where D is a positive integer with square free.