High School Number Theory Archives - Page 5 of 11

Triangular Numbers and the Sum of the First n Positive Integers

June 16, 2012 GB High School Mathematics, High School Number Theory

The numbers 1, 3, 6, 10, 15, … are called triangular numbers because they could be arranged in the form of triangles. Triangular numbers is one of the polygonal numbers — numbers that can represented by dots to form regular polygons.

Finding the nth triangular number is quite easy. All we have to do is form a rectangle using the “dot representation” of two triangular numbers. For example, we want to find the fourth triangular number, we create dots representing two triangular numbers, and then use them to form a rectangle. The area of the formed rectangle is $4(4+1)$ . » Read more

Prime or Not: Determining Primes Through Square Root

June 2, 2012 GB High School Mathematics, High School Number Theory

A prime number is a integer greater than that is divisible only by 1 and itself. A number that is not prime is composite.

To determine whether a number is prime or not, we have to divide it by all numbers between 1 and itself . For example, to say that 257 is prime, we must be sure that it is not divisible by any number between 1 and 257. In this discussion, the word “numbers” refer to positive integers.

Are you prime or not?

Dividing a number by all numbers between 1 and itself is burdensome especially for large numbers. In this post, we discuss a shorter way of determining if a number is prime and explain why the method works. » Read more

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Proof of the Sum of Square Numbers

May 27, 2012 GB High School Mathematics, High School Number Theory

In the first part of this series, we have counted the number of squares on a chessboard, and we have discovered that it is equal to the sum of the squares of the first 8 positive integers. The numbers $1^2$ , $2^2$ , $3^2$ and so on are called square numbers.

This method can be generalized to compute for the number of squares on larger square boards. If the measure of a board is $n \times n$ , then the number of squares on it is » Read more

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