In number theory, the sum of the first n cubes is the square of the nth triangular number. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n ) 2...

mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a square number. There are infinitely...

number, other examples being square numbers and cube numbers. The nth triangular number is the number of dots in the triangular arrangement with n dots on...

squared". The name square number comes from the name of the shape. The unit of area is defined as the area of a unit square (1 × 1). Hence, a square with...

properties of oblong, triangular, and square numbers: 1 . The number 10 for example, can be arranged as a triangle (see triangular number): But 10 cannot be...

non-trivial square triangular number. Aside from being the smallest square triangular number other than 1, it is also the only triangular number (other than...

As well as being used to approximate the square root of two, Pell numbers can be used to find square triangular numbers, to construct integer approximations...

A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other...

152), an octagonal number, and a squared triangular number (225 = (1 + 2 + 3 + 4 + 5)2 = 13 + 23 + 33 + 43 + 53) . As the square of a double factorial...

A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. The term often refers to square pyramidal numbers...

n-th square pyramidal number. The number of rectangles in a square grid is given by the squared triangular numbers. The square pyramidal number P n {\displaystyle...

triangular number 1,544,804,416 = 393042 = 11563 = 346 1,564,031,349 = 695 1,606,879,040 : Dowling number 1,631,432,881 = 403912, square triangular number...

n} th triangular number, then the doubly triangular numbers are the numbers of the form T T n {\displaystyle T_{T_{n}}} . The doubly triangular numbers...

A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron...

The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes...

A truncated triangular pyramid number is found by removing (truncating) some smaller tetrahedral number (or triangular pyramidal number) from each of...

has a different quotient 1785 = square pyramidal number, triangular matchstick number 1786 = centered triangular number 1787 = super-prime, sum of eleven...

multiplication table gives the Nicomachus theorem, proving that each squared triangular number is a sum of cubes. In an acute isosceles triangle, it is possible...

A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular and square numbers to the nonagon (a nine-sided...

{\displaystyle 1^{3}+2^{3}+\cdots +n^{3}=(1+2+\cdots +n)^{2}} (see squared triangular number) Aryabhata's system of astronomy was called the audAyaka system...

right triangular prism is semiregular. A semiregular prism means that the number of its polygonal base's edges equals the number of its square faces....

the only triangular Fibonacci numbers, which was conjectured by Vern Hoggatt and proved by Luo Ming. No Fibonacci number can be a perfect number. More generally...

In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center...

are both tetrahedral and square pyramidal. Square triangular number, the numbers that are simultaneously square and triangular Close-packing of equal spheres...

605 = 5 × 112, Harshad number, sum of the nontriangular numbers between the two successive triangular numbers 55 and 66, number of non-isomorphic set-systems...

such representations of the number 17, for example, are shown below: 17 = 10 + 6 + 1 (triangular numbers) 17 = 16 + 1 (square numbers) 17 = 12 + 5 (pentagonal...

A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns...

55 is the tenth triangular number, it is also the tenth Fibonacci number, and the largest such number to also be a triangular number. 55 is also the fourth...

Since 36 is also triangular, 666 is a doubly triangular number. Also, 36 = 15 + 21 where 15 and 21 are triangular as well, whose squares (152 = 225 and...

divides the Euclid number 2999# + 1 3003 – triangular number, only number known to appear eight times in Pascal's triangle; no number is known to appear...