enow.com Web Search

Search results

1. Results from the WOW.Com Content Network

2. Fermat's theorem on sums of two squares - Wikipedia

   en.wikipedia.org/wiki/Fermat's_theorem_on_sums_of...

   For the avoidance of ambiguity, zero will always be a valid possible constituent of "sums of two squares", so for example every square of an integer is trivially expressible as the sum of two squares by setting one of them to be zero. 1. The product of two numbers, each of which is a sum of two squares, is itself a sum of two squares.

3. Sum of squares - Wikipedia

   en.wikipedia.org/wiki/Sum_of_squares

   Legendre's three-square theorem states which numbers can be expressed as the sum of three squares; Jacobi's four-square theorem gives the number of ways that a number can be represented as the sum of four squares. For the number of representations of a positive integer as a sum of squares of k integers, see Sum of squares function.

4. Sum of two squares theorem - Wikipedia

   en.wikipedia.org/wiki/Sum_of_two_squares_theorem

   Therefore, the theorem states that it is expressible as the sum of two squares. Indeed, 2450 = 7 2 + 49 2. 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.

5. Legendre's three-square theorem - Wikipedia

   en.wikipedia.org/wiki/Legendre's_three-square...

   Pierre de Fermat gave a criterion for numbers of the form 8a + 1 and 8a + 3 to be sums of a square plus twice another square, but did not provide a proof. [1] N. Beguelin noticed in 1774 [2] that every positive integer which is neither of the form 8n + 7, nor of the form 4n, is the sum of three squares, but did not provide a satisfactory proof. [3]

6. Nesbitt's inequality - Wikipedia

   en.wikipedia.org/wiki/Nesbitt's_inequality

   1.3 Third proof: Sum of Squares. 1. ... every rational inequality can be demonstrated by transforming it to the appropriate sum-of-squares ... Online e-book in PDF ...

7. Euler's factorization method - Wikipedia

   en.wikipedia.org/wiki/Euler's_factorization_method

   The Brahmagupta–Fibonacci identity states that the product of two sums of two squares is a sum of two squares. Euler's method relies on this theorem but it can be viewed as the converse, given n = a 2 + b 2 = c 2 + d 2 {\displaystyle n=a^{2}+b^{2}=c^{2}+d^{2}} we find n {\displaystyle n} as a product of sums of two squares.