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The sum of squares is not factorable. The squared Euclidean distance between two points, equal to the sum of squares of the differences between their coordinates. Heron's formula for the area of a triangle can be re-written as using the sums of squares of a triangle's sides (and the sums of the squares of squares)
In mathematics, Legendre's three-square theorem states that a natural number can be represented as the sum of three squares of integers. if and only if n is not of the form for nonnegative integers a and b. Distances between vertices of a double unit cube are square roots of the first six natural numbers due to the Pythagorean theorem (√7 is ...
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. is a Bernoulli polynomial. is an Euler number. is the Riemann zeta function. is the gamma function. is a polygamma function. is a polylogarithm.
Its exponent in the decomposition, 2, is even. Therefore, the theorem states that it is expressible as the sum of two squares. Indeed, 2450 = 72 + 492. The prime decomposition of the number 3430 is 2 · 5 · 7 3. This time, the exponent of 7 in the decomposition is 3, an odd number. So 3430 cannot be written as the sum of two squares.
In number theory, the sum of squares function is an arithmetic function that gives the number of representations for a given positive integer n as the sum of k squares, where representations that differ only in the order of the summands or in the signs of the numbers being squared are counted as different. It is denoted by rk(n).
In additive number theory, Fermat 's theorem on sums of two squares states that an odd prime p can be expressed as: with x and y integers, if and only if. The prime numbers for which this is true are called Pythagorean primes. For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and they can be expressed as sums of ...
A Pythagorean prime is a prime number of the form . Pythagorean primes are exactly the odd prime numbers that are the sum of two squares; this characterization is Fermat's theorem on sums of two squares. Equivalently, by the Pythagorean theorem, they are the odd prime numbers for which is the length of the hypotenuse of a right triangle with ...
The numbers whose trajectory under iteration of sum of squares of digits map includes 1. A007770: Factorial primes: 2, 3, 5, 7, 23, 719, 5039, 39916801, ... A prime number that is one less or one more than a factorial (all factorials > 1 are even). A088054: Wolstenholme primes: 16843, 2124679