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Square number. Square number 16 as sum of gnomons. In mathematics, a square number or perfect square is an integer that is the square of an integer; [ 1] in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 32 and can be written as 3 × 3 .
25 is the sum of the five consecutive single-digit odd natural numbers 1, 3, 5, 7, and 9. 25 is a centered octagonal number, [ 1] a centered square number, [ 2] a centered octahedral number, [ 3] and an automorphic number. [ 4] 25 percent (%) is equal to 1 4 . It is the smallest decimal Friedman number as it can be expressed by its own ...
Square (algebra) 5⋅5, or 52 (5 squared), can be shown graphically using a square. Each block represents one unit, 1⋅1, and the entire square represents 5⋅5, or the area of the square. In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation.
Every centered square number except 1 is the hypotenuse of a Pythagorean triple (3-4-5, 5-12-13, 7-24-25, ...). This is exactly the sequence of Pythagorean triples where the two longest sides differ by 1.
The palindromic square numbers are 0, 1, 4, 9, 121, 484, 676, 10201, ... n even with an odd number of prime factors 1 2 9 21 100 180 ... 1 4 25 39 205 303
Primes p for which p − 1 divides the square of the product of all ... Primes p that divide 2 n − 1, for some prime number n. 3, 7, 23 ... 25 p − 1 ≡ 1 (mod p ...
Thus a pronic number is squarefree if and only if n and n + 1 are also squarefree. The number of distinct prime factors of a pronic number is the sum of the number of distinct prime factors of n and n + 1. If 25 is appended to the decimal representation of any pronic number, the result is a square number, the square of a number ending on 5; for ...
Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers, starting with the 0th triangular number ...