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A positive integer that can be written as the sum of two or more consecutive positive integers. A138591: Erdős–Nicolas numbers: 24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, ... A number n such that there exists another number m and , =. A194472: Solution to Stepping Stone Puzzle
To find integer solutions to + =, find positive integers r, s, and t such that = is a perfect square. Then: = +, = +, = + +. From this we see that r is any even integer and that s and t are factors of r 2 /2. All Pythagorean triples may be found by this method.
The transitivity of M implies that the integers and integer sequences inside M are actually integers and sequences of integers. An integer sequence is a definable sequence relative to M if there exists some formula P ( x ) in the language of set theory, with one free variable and no parameters, which is true in M for that integer sequence and ...
Gaussian integers are complex numbers of the form α = u + vi, where u and v are ordinary integers and i is the square root of negative one. The units of Gaussian integers are ±1 and ±i. The ordinary integers are called the rational integers and denoted as ' Z '. The Gaussian integers are denoted as Z[i].
In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition.
The Euclidean algorithm can be thought of as constructing a sequence of non-negative integers that begins with the two given integers = and = and will eventually terminate with the integer zero: {=, =, , , , , =} with + <.
Subsequences can contain consecutive elements which were not consecutive in the original sequence. A subsequence which consists of a consecutive run of elements from the original sequence, such as ,, , from ,,,,, , is a substring. The substring is a refinement of the subsequence.
In newer language versions the distinction is completely gone and all integers behave like arbitrary-length integers. Python supports normal floating point numbers, which are created when a dot is used in a literal (e.g. 1.1), when an integer and a floating point number are used in an expression, or as a result of some mathematical operations ...