We investigate the number and the set structure of the solutions of a consistent system of random equations of the form [This equation cannot be converted into ASCII Text.] with respect to the variables x[SUB1],..., x[SUBn] ξ{0,..., q-1}, q ≥ 2, where the indices s[SUB1]...
Describe how to determine the number of solutions that a system of equations has (one, none, or infinite).
A. G. Kushnirenko, "A Newton polyhedron and the number of solutions of a system of k equations in k unknowns," Usp. Matem. Nauk,30, No. 2, 266–267 (1975). About this Article Title The number of roots of a system of equations Journal Functional Analysis and Its Applications Vol...
The equations x+y+z=6 x+2y+3z=10 x+2y+mz=n given infinite numb... 03:20 The system of equations 2x-y+z=0 x-2y+z=0 x-y+2z=0 has infinite ... Text Solution The system of equations a1x+b1y+c1z=0 a2x+b2y+c2z=0 a3x+b3y+c3z... 01:26 Can the inverse of the foll...
Note that, if the last condition is not satisfied, then A2/A1 = D2/D1 = q 2 for some q ∈ Q and the solutions (X, Y, Z) of the system of equations are given by (X, Y, qX), where (X, Y ) is a solution of the first equation of the system. A large number of papers...
The number of solutions of a nonlinear system of equations over the Galois field F = GF (2 m ) is expressed in terms of Kloosterman sums over the Galois fi... T Helleseth,VA Zinoviev - 《Discrete Mathematics》 被引量: 13发表: 2004年 Recursive formulas generating power moments of multi-...
Example 22:AMC)The number of real solutions17(x,y,z,w)of the simultaneous equations 2y =x2z=y+17,20=z+17,2x=w+17is().17(A)1(B)2(C)4(D)8(E)16Example 22:(AMC)The number of real solutions (x,y,z,w)of the simultaneous equations 2y =x+ 172z=y+y 172W=2+ 172x=W...
Let xx ' ≡1(modn). The authors find an explicit formula for the number N(n) of solutions (k 1 ,k 2 ,k 3 ,k 4 ) of k 1 +k 2 ≡k 3 +k 4 (modn), k 1 ' +k 2 ' ≡k 3 ' +k 4 ' (modn) in the reduced system of residues. It is shown that N is a multiplic...
T. Tambour, The number of solutions of some equations in finite groups and a new proof of Itos theorem, Commun. Algebra 28(11) (2000) 5353- 5362.T. Tambour. The number of solutions of some equations in finite groups and a new proof of ito's theorem. Comm. Algebra, 28:5353-5361, ...
Let a and b be positive integers.In this paper,we study the number of positive integers solutions(x,y,z) of the simultaneous Diophantine equations x~2-ay~2=1,y~2-bz~2=1. It is proved that if a=2,the above equations possesses at most one positive integer solution(x,y,z). This ...