Hardness of a system of integer quadratic equations - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-25T06:08:06Z http://mathoverflow.net/feeds/question/90781 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/90781/hardness-of-a-system-of-integer-quadratic-equations Hardness of a system of integer quadratic equations unknown (google) 2012-03-10T01:06:26Z 2012-03-10T01:06:26Z <p>What is the hardness (NP or P) of the following system of quadratic equations in positive integers $a_i$ and $b_i$</p> <p>$\sum_{i=1}^{N}(a_i+ b_i)^2 = k_1$</p> <p>$\sum_{i=1}^{N} a_i = k_2$ </p> <p>$\sum_{i=1}^{N} b_i = k_3$, where $k_1$, $k_2$ and $k_3$ are constants.</p> <p>What is the hardness (NP or P) of the following systems of quadratic equations in positive integers $a_i$ and $b_i$?</p> <p>$m \sum_{i=1}^{N} b_i + n \sum_{i=1}^{N}(a_i+ b_i)^2 = k_1$</p> <p>$\sum_{i=1}^{N}(a_i+ b_i) = k_2$, where $m$, $n$, $k_1$ and $k_2$ are constants.</p>