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 1d awarded Notable Question Apr15 comment Cardinality of solutions for a set of linear equations @Travis how there are not linear since A=BC? Apr15 comment Cardinality of solutions for a set of linear equations Well from Travis's observation that BC=A it is quite obvious that the bound i am looking for all the different number of solutions is C(n,N) All the possible combinations of n elements out of N. Right? since the equations are linear dependent.As such any possible combinations of $x_i$ work Apr15 comment Cardinality of solutions for a set of linear equations @Travis Well i am missing some theory because i cannot interpret why in curves $n=4$ where n is the possible elements of a curve. Apr15 comment Cardinality of solutions for a set of linear equations Yes but $0 \notin \mathbb{F}_q^*$, since it is a field every element has multiplicative inverse so 0 is not part of it Apr15 comment Cardinality of solutions for a set of linear equations @Travis Yes, actually $B=AC^{-1}$ Apr15 comment Cardinality of solutions for a set of linear equations I guess the solutions for $x_1$ are all the possible elements in the field. But once $x_1$ is fixed this restricts the values of $x_2$ and $x_3$. Right? Apr15 comment Cardinality of solutions for a set of linear equations It is not somehow dictated by the set of equations which are 3? Apr15 comment Cardinality of solutions for a set of linear equations Is there a bounded formula for the number of possible solutions?are there some constants A,B,C that give different number of possible solutions than other? Apr15 revised Cardinality of solutions for a set of linear equations deleted 29 characters in body Apr15 comment Cardinality of solutions for a set of linear equations @MarcvanLeeuwen i changed the question since it was wrong. Apr15 revised Cardinality of solutions for a set of linear equations added 36 characters in body Apr15 comment Cardinality of solutions for a set of linear equations @MarcvanLeeuwen they lie in a finite field: $x_i \in F_N^*$ Apr15 comment Cardinality of solutions for a set of linear equations Maybe the question was not clear. Given $A,B,C$. How many different sets of x_i satisfy this? Apr15 asked Cardinality of solutions for a set of linear equations Mar30 revised What is the probability of the sum of elements in $\mathbb{Z}_{N^2}^*$ to be multiplicatively inverted? added 43 characters in body Mar30 asked What is the probability of the sum of elements in $\mathbb{Z}_{N^2}^*$ to be multiplicatively inverted? Jan28 awarded Tumbleweed Jan21 asked Divisibility property of Laplace Nov21 answered Bilinear Map vs Inner Product