121 (one hundred ndtwenty-one) is the

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

following 120 and preceding 122.

In mathematics

''One hundred ndtwenty-one'' is * a

square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

(11 times 11) * the sum of the powers of 3 from 0 to 4, so a repunit in ternary. Furthermore, 121 is the only square of the form

1 + p + p^2 + p^3 + p^4

, where ''p'' is prime (3, in this case). * the sum of three consecutive

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

s (37 + 41 + 43). * As

5! + 1 = 121

, it provides a solution to Brocard's problem. There are only two other squares known to be of the form

n! + 1

. Another example of 121 being one of the few numbers supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form

x^-4

(with being 2 and 5, respectively).Wells, D., '' The Penguin Dictionary of Curious and Interesting Numbers'', London: Penguin Group. (1987): 136 * It is also a star number, a centered tetrahedral number, and a

centered octagonal number A centered octagonal number is a centered number, centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are th ...

* In decimal, it is a Smith number since its digits add up to the same value as its factorization (which uses the same digits) and as a consequence of that it is a

Friedman number A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷), additive inverses, ...

(

11^2

). But it cannot be expressed as the sum of any other number plus that number's digits, making 121 a self number.

References

Integers {{Num-stub