On the Diophantine Equation
نویسندگان
چکیده
= c for some integers a, b, c with ab 6= 0, has only finitely many integer solutions. Stoll & Tichy proved more generally that if a, b, c ∈ Q and ab 6= 0, then for m > n ≥ 3, the above equation has only finitely many integral solutions x, y. Independently, Rakaczki established a more precise finiteness result on this binomial equation and extended this result to more general equations (see Acta Arith. 110(2003), 339-360 and Periodica Math. Hungar. 49(2004), 119-132). Another natural example comes from counting lattice points in generalized octahedra. The number of integral points on the n-dimensional octahedron |x1| + |x2|+ · · · + |xn| ≤ r is given by the expression pn(r) = ∑n i=0 2 i ( n i )( r i )
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