Solution Linear EquationsExample 2: Consider the equation 9(x – 1) – 35 = 8x + 37 On solving we have 9x – 9 – 35 = 8x + 37 Collect the like terms on both sides by transferring them, we have Linear equations with one, zero, or infinite solutions The Solution of System of Linear Equations A solution for a system of linear
1 Equations satisfied by all solutions of linear equations THEOREM 2 If a non-linear homogeneous algebraic difference equation of the m-th order is satisfied by all the solutions of a linear difference equation I (3) Y,ai (x)y (x +i) =0, (:E ), j=O where ao (x), a, (x), , al(x) are polynomials in x, then, it mnay be written in the form m-1 1
Commun Math Phys 193, 373–396 (1998) Communications in Mathematical Physics © Springer-Verlag 1998 Elliptic Solutions to Difference Non-Linear Equations and
many equations, and show how such systems can be thrown into the form of systems of contour integral equations in the complex plane These integral equations are then inverted: we obtain solutions which are themselves contour integrals * The method employs the Laplace transformation f
equation vn = vm admits only finitely many solutions n ^ m with n, m > 0 Laurent [2] obtained qualitative results about equations v„ = Xvm and more generally about equations (1 5) A complete qualitative characterization of the set of solutions of such equations is given in Schlickewei and Schmidt [7] For