ფაილების კატალოგი

Theorem 1. Let a Diophantine equation (x-a)ⁿ(xⁿ-yⁿ)=bⁿxⁿ. If n>2 then the equation has no a solution; if n<=2 then the equation has the solution.

Theorem 2. Let the Diophantine equation (x-a)ⁿ(xⁿ+yⁿ)=bⁿxⁿ. If n>2 then the equation has no the solution; if n=1 then the equation has the solution; if n=2 then the equation has the solution in the case without when there exists r natural number and 4k+3 kind of prime number p|b such that p^2r-1|b and p^2r|b (where the solution has not).

                                                                Emzari Papava