- #1
ramsey2879
- 841
- 3
Find all a,b such that a*T(b) + b^2*T(a-1) = b*T(a) + a^2*T(b-1)
example solution a = 3, b = 7
example solution a = 3, b = 7
Triangular numbers are a sequence of numbers where the pattern forms an equilateral triangle. Each number in the sequence is the sum of all the natural numbers from 1 to n, where n is the position of the number in the sequence.
The formula for finding the nth triangular number is n(n+1)/2. For example, the 5th triangular number would be (5x6)/2 = 15.
Triangular numbers have been studied for centuries and have many applications in mathematics, such as in Pascal's triangle and in geometric series. They also have connections to real-world phenomena, such as the number of objects in a triangular arrangement.
One interesting property is that every positive integer can be expressed as the sum of two or more consecutive triangular numbers. Another is that the difference between consecutive triangular numbers is always a perfect square.
Triangular numbers have applications in many areas of science, such as in physics for calculating the number of atoms in a triangular lattice and in computer science for optimizing algorithms. They also have connections to music, art, and architecture.