1

One (1) is a positive integer one more than 0 and one less than 2.

Properties
One is the only positive integer that is neither a prime number nor a composite number.

Any number multiplied by itself is the other number, that is, 1*n = n.

Any number to the power of 1 is itself, or in other words, n^1 = n. And one to any power is 1, so 1n = 1.

One is the first in many sequences. It is the first square number (next is 4), cube number (next is 8), Fibonacci number (also the second one, next is 2), triangular number (next is 3), Lucas number (next is 3), tetrahedral number (next is 4), factorial number (next is 2), square pyramidal number (next is 5), pentatope number (next is 5), lucky number (next is 3), highly composite number (next is 2), deficient number, fourth power (next is 16), and many, many more. Many of these properties are trivial. It is also the only number that can be divided into any integer, as x/1 = x.

Logarithms on base 1 are undefined, as 1^x is always 1. The 1st root of a number is always just the original number.