Squares in number theory | Diophantine equations | Integer sequences | Theorems in number theory
In number theory, a congruum (plural congrua) is the difference between successive square numbers in an arithmetic progression of three squares.That is, if , , and (for integers , , and ) are three square numbers that are equally spaced apart from each other, then the spacing between them, , is called a congruum. The congruum problem is the problem of finding squares in arithmetic progression and their associated congrua. It can be formalized as a Diophantine equation: find integers , , and such that When this equation is satisfied, both sides of the equation equal the congruum. Fibonacci solved the congruum problem by finding a parameterized formula for generating all congrua, together with their associated arithmetic progressions. According to this formula, each congruum is four times the area of a Pythagorean triangle. Congrua are also closely connected with congruent numbers: every congruum is a congruent number, and every congruent number is a congruum multiplied by the square of a rational number. (Wikipedia).
Number Theory | Congruence Modulo n -- Definition and Examples
We define the notion of congruence modulo n among the integers. http://www.michael-penn.net
From playlist Modular Arithmetic and Linear Congruences
Triangle Congruence (quick review)
More resources available at www.misterwootube.com
From playlist Further Properties of Geometrical Figures
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
What is the Definition of Congruent Triangles - Congruent Triangles
👉 Learn about congruent triangles theorems. Two or more triangles (or polygons) are said to be congruent if they have the same shape and size. There are many methods to determine whether two triangles are congruent. Some of the methods include: (1) The SSS (Side Side Side) congruency the
From playlist Congruent Triangles
Number Theory | Some properties of integer congruence.
We examine some basic properties of congruence modulo n among the integers.
From playlist Modular Arithmetic and Linear Congruences
Congruent and Similar Triangles
working with similiar triangles, determining similar triangles http://mathispower4u.wordpress.com/
From playlist Geometry Basics
Number Theory - Basics of Congruences
From playlist â„•umber Theory
What is an Included Side of a Triangle - Congruent Triangles
👉 Learn about the included angles of a triangle. An included angle of a triangle is the angle between two sides of a triangle. An included side of a triangle is the side between two angles. To show that two triangles are congruent by the side angle side (SAS) congruency theorem, we must s
From playlist Congruent Triangles
In this video we continue discussing congruences and, in particular, we discuss solutions of linear congruences. The content of this video corresponds to Section 4.4 of my book "Number Theory and Geometry" which you can find here: https://alozano.clas.uconn.edu/number-theory-and-geometry/
From playlist Number Theory and Geometry
What are congruent polygons - Congruent Triangles
👉 Learn about congruent triangles theorems. Two or more triangles (or polygons) are said to be congruent if they have the same shape and size. There are many methods to determine whether two triangles are congruent. Some of the methods include: (1) The SSS (Side Side Side) congruency the
From playlist Congruent Triangles
Pythagoras twisted squares: Why did they not teach you any of this in school?
A video on the iconic twisted squares diagram that just about anybody who knows anything about mathematics has been familiar with since primary school. Surprisingly, there is a LOT more to this diagram than even expert mathematicians are aware of. And lots of this LOT is really really beau
From playlist Recent videos