algebra   4791

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mathedu  algebra 
2 days ago by Cmmc97
[math/0609127] Square Eulerian Quadruples
We consider the problem of finding 4 rational squares, such that the product of any two plus the sum of the same two always gives a square. We give some historical background and exhibit one such quadruple.
number-theory  algebra  constraint-satisfaction  rather-interesting  nudge-targets  consider:performance-measures  algorithms 
6 days ago by Vaguery
[0909.1666] On Sets of Integers where Each Pair Sums to a Square
We discuss the problem of finding distinct integer sets {x1,x2,...,xn} where each sum xi+xj,i≠j is a square, and n≤7. We confirm minimal results of Lagrange and Nicolas for n=5 and for the related problem with triples. We provide new solution sets for n=6 to add to the single known set. This provides new information for problem D15 in Guy's {\it Unsolved Problems in Number Theory}
number-theory  algebra  constraint-satisfaction  open-problems  nudge-targets  consider:looking-to-see 
6 days ago by Vaguery
[1006.3153] Perfect Quadrilateral Right Prisms
We consider right prisms with horizontal quadrilateral bases and tops, and vertical rectangular sides. We look for examples where all the edges, face diagonals and space diagonals are integers. We find examples when the base is an isosceles trapezium and a parallelogram, but no solution for a kite or rhombus.
number-theory  algebra  constraint-satisfaction  catalog  nudge-targets  consider:looking-to-see 
6 days ago by Vaguery
[1109.2396] New Solutions of $d=2x^3+y^3+z^3$
We discuss finding large integer solutions of d=2x3+y3+z3 by using Elsenhans and Jahnel's adaptation of Elkies' LLL-reduction method. We find 28 first solutions for |d|<10000.
number-theory  algebra  polynomials  constraint-satisfaction  rather-interesting  to-write-about  nudge-targets  consider:looking-to-see  stamp-collecting  algorithms 
6 days ago by Vaguery
[1312.1793] "Nice" Rational Functions
We consider simple rational functions Rmn(x)=Pm(x)/Qn(x), with Pm and Qn polynomials of degree m and n respectively. We look for "nice" functions, which we define to be ones where as many as possible of the roots, poles, critical points and (possibly) points of inflexion are integer or, at worst, rational.
algebra  number-theory  rather-interesting  constraint-satisfaction  stamp-collecting  nudge-targets  consider:looking-to-see  consider:feature-discovery 
6 days ago by Vaguery
Graphical Linear Algebra
  And because arithmetic science and geometric science are connected, and support one another, the full knowledge of numbers cannot be presented without encountering some geometry, or without seeing that operating in this way on numbers is close to geometry; the method is full of many proofs and demonstrations that are made with geometric figures.…
compsci  math  algebra 
6 days ago by geetarista

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