What is the maximum possible number of solutions of homogeneous system N &#x00D7;<!-- × -->

mravinjakag

mravinjakag

Answered question

2022-06-05

What is the maximum possible number of solutions of homogeneous system N × N ( N variables, N equations) of degree 2, where in each equation we have linear terms in x i and quadratic terms in x i x j , for i j, but not quadratic terms in x i 2 ?

Answer & Explanation

Leland Ochoa

Leland Ochoa

Beginner2022-06-06Added 25 answers

The system of equations equation x 2 i ( 2 k 1 ) x 2 i = 0 where k ranges from 1 to n, has infinitely many solutions, namely when all the even (resp odd) indices are 0, and the odd (resp even) can be anything you want. (There are possibly other solutions, which I do not care for.) Hence, you can have infinitely many solutions.
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