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  2. Proof of Fermat's Last Theorem for specific exponents

    en.wikipedia.org/wiki/Proof_of_Fermat's_Last...

    Since u and v are coprime, the greatest common divisor of 2u and u 2 + 3v 2 is either 1 (case A) or 3 (case B). Proof for case A. In this case, the two factors of −z 3 are coprime. This implies that three does not divide u and that the two factors are cubes of two smaller numbers, r and s. 2u = r 3 u 2 + 3v 2 = s 3. Since u 2 + 3v 2 is odd ...

  3. 1 + 2 + 3 + 4 + ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E...

    The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...

  4. 1 − 2 + 3 − 4 + ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%E2%88%92_2_%2B_3_%E2%88...

    The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.

  5. Arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arithmetic

    The main arithmetic operations are addition, subtraction, multiplication, and division. Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms .

  6. Prime number - Wikipedia

    en.wikipedia.org/wiki/Prime_number

    A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...

  7. List of prime numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_prime_numbers

    Also called primes congruent to d modulo a . The primes of the form 2 n +1 are the odd primes, including all primes other than 2. Some sequences have alternate names: 4 n +1 are Pythagorean primes, 4 n +3 are the integer Gaussian primes, and 6 n +5 are the Eisenstein primes (with 2 omitted).

  8. Number line - Wikipedia

    en.wikipedia.org/wiki/Number_line

    In advanced mathematics, the number line is usually called the real line or real number line, and is a geometric line isomorphic to the set of real numbers, with which it is often conflated; both the real numbers and the real line are commonly denoted R or ‍ ‍. The real line is a one- dimensional real coordinate space, so is sometimes ...

  9. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or ‍ ‍, where a and b are both integers. [9] As with other fractions, the denominator ( b) cannot be zero. Examples include 1 2, − 8 5, −8 5, and 8 −5.

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