Additive number theory | Squares in number theory | Theorems in number theory
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 two squares in the following ways: On the other hand, the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares. This is the easier part of the theorem, and follows immediately from the observation that all squares are congruent to 0 or 1 modulo 4. Since the Diophantus identity implies that the product of two integers each of which can be written as the sum of two squares is itself expressible as the sum of two squares, by applying Fermat's theorem to the prime factorization of any positive integer n, we see that if all the prime factors of n congruent to 3 modulo 4 occur to an even exponent, then n is expressible as a sum of two squares. The converse also holds. This generalization of Fermat's theorem is known as the sum of two squares theorem. (Wikipedia).
Sum of integers squared explained
Explanation on deriving the equation. In arithmetic, we often come across the sum of n natural numbers. Sum of squares refers to the sum of the squares of numbers. It is basically the addition of squared numbers. Support my channel with this special custom merch! https://www.etsy.com/list
From playlist Math formulas, proofs, ideas explained
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NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Leibniz's formula pi/4 = 1-1/3+1/5-1/7+... is one of the most iconic pi formulas. It is also one of the
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From playlist Solve Quadratic Equations by Factoring | Difference of Two Squares
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From playlist Solve Quadratic Equations by Factoring | Difference of Two Squares
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From playlist Solve Quadratic Equations by Factoring | Difference of Two Squares
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From playlist Solve Quadratic Equations by Factoring | Difference of Two Squares
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From playlist CTNT 2022 - Conference lectures and special guest lectures
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From playlist Solve Quadratic Equations by Factoring | Difference of Two Squares