All ways to express a given positive integer as the sum of three fifth ...
Dec 25, 2025 · If N is Cong to 4,5,6,7 mod 11 then N cant be written as sum of three fifth powers over Z. If N is Cong to 5,6 mod 11 then N can't be written as sum of four Fifth powers over Z. So more than …
geometry - Explain why a line can never intersect a plane in exactly ...
Jun 16, 2019 · Common sense approach: take a straight piece of paper, assume it represents a plane. Take a pencil, assume it represents a line. Since the line is not "curved", it can intersect with the …
quadratics - Newton's Identity - Mathematics Stack Exchange
Jul 10, 2021 · While reading about quadratic equations, I came across Newton's Identity formula which said we can express αn +βn α n + β n in simpler forms but not given any explanation. They wrote Sn …
functional analysis - The resolvent set for unbounded operators ...
Jul 30, 2025 · I am interested in the resolvent set (and spectrum) of unbounded operators. In the case of bounded linear operators one defines the resolvent set to be the collection of $\\lambda \\in …
Geometry notation: what does $m\\angle ABC$ mean?
@Hilbert: As blf points out, ∠ABC ∠ A B C denotes the angle, itself, while m∠ABC m ∠ A B C is its measure. For example, suppose we have an equilateral triangle with vertices A, B, C. A, B, C Then …
Notations involving squiggly lines over horizontal lines
Sep 28, 2011 · Is there a symbol for "homeomorphic to"? I looked on Wikipedia, but it doesn't seem to mention one? Also, for isomorphism, is the symbol a squiggly line over an equals sign? What is the …
Difference between Adjoint of a matrix and its transpose
Jan 9, 2020 · where t t denotes transpose of a matrix. My Question is that then from above equality the notions of transpose of a matrix and adjoint of a matrix are same, they why we use separate …
Compound Interest Formula adding annual contributions
Mar 15, 2016 · I'd like to know the compound interest formula for the following scenario: P = Initial Amount i = yearly interest rate A = yearly contribution or deposit added. n = the deposits will be …
What is the minimum and maximum number of eigenvectors?
May 14, 2015 · I am given the eigenvalues of a square, 8x8, matrix. They are all non-zero. I have determined that the matrix is diagonalizable and has an inverse. In one part of the problem, I am …
algebraic geometry - Why is a smooth connected scheme irreducible ...
More generally, locally with finitely many irreducible components is enough (each point has a neighborhood with finitely many irreducible components). The full statement is then "every regular, …