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  2. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    Graphs of y = b x for various bases b: base 10, base e, base 2, base ⁠ 1 / 2 ⁠. Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.

  3. Fourth power - Wikipedia

    en.wikipedia.org/wiki/Fourth_power

    Fermat knew that a fourth power cannot be the sum of two other fourth powers (the n = 4 case of Fermat's Last Theorem; see Fermat's right triangle theorem). Euler conjectured that a fourth power cannot be written as the sum of three fourth powers, but 200 years later, in 1986, this was disproven by Elkies with: 20615673 4 = 18796760 4 ...

  4. Algebraic operation - Wikipedia

    en.wikipedia.org/wiki/Algebraic_operation

    The plus–minus sign, ±, is used as a shorthand notation for two expressions written as one, representing one expression with a plus sign, the other with a minus sign. For example, y = x ± 1 represents the two equations y = x + 1 and y = x − 1. Sometimes, it is used for denoting a positive-or-negative term such as ±x.

  5. Power of two - Wikipedia

    en.wikipedia.org/wiki/Power_of_two

    The only known powers of 2 with all digits even are 2 1 = 2, 2 2 = 4, 2 3 = 8, 2 6 = 64 and 2 11 = 2048. [12] The first 3 powers of 2 with all but last digit odd is 2 4 = 16, 2 5 = 32 and 2 9 = 512. The next such power of 2 of form 2 n should have n of at least 6 digits.

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

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

    Let the right triangle have sides (u, v, w), where the area equals ⁠ uv / 2 ⁠ and, by the Pythagorean theorem, u 2 + v 2 = w 2. If the area were equal to the square of an integer s ⁠ uv / 2 ⁠ = s 2. then by algebraic manipulations it would also be the case that 2uv = 4s 2 and −2uv = −4s 2. Adding u 2 + v 2 = w 2 to these equations gives

  7. Factorial - Wikipedia

    en.wikipedia.org/wiki/Factorial

    1 1: 1 2: 2 3: 6 4: 24 5: 120 6: 720 7: 5 040: 8: 40 320: 9: 362 880: 10: 3 628 800: 11: 39 916 800: 12: 479 001 600: 13: 6 227 020 800: 14: 87 178 291 200: 15: 1 307 674 368 000: 16: 20 922 789 888 000: 17: 355 687 428 096 000: 18: 6 402 373 705 728 000: 19: 121 645 100 408 832 000: 20: 2 432 902 008 176 640 000: 25 1.551 121 004 × 10 25: 50 ...

  8. Multiplicative inverse - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_inverse

    For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution).

  9. Square (algebra) - Wikipedia

    en.wikipedia.org/wiki/Square_(algebra)

    For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 + 2x + 1. One of the important properties of squaring, for numbers as well as in many other mathematical systems, is that (for all numbers x), the square of x is the same as the square of its additive inverse −x.

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