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  2. 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. [11] 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.

  3. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    Powers of 2 appear in set theory, since a set with n members has a power set, the set of all of its subsets, which has 2 n members. Integer powers of 2 are important in computer science. The positive integer powers 2 n give the number of possible values for an n-bit integer binary number; for example, a byte may take 2 8 = 256 different values.

  4. Sums of powers - Wikipedia

    en.wikipedia.org/wiki/Sums_of_powers

    In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.

  5. Subscript and superscript - Wikipedia

    en.wikipedia.org/wiki/Subscript_and_superscript

    2 is a divalent cation of carbon with 14 nucleons, of which six are protons and 8 are neutrons, and there are two atoms in this chemical compound. The numerators of stacked fractions (such as ⁠ 34 / 35 ⁠ ) usually use high-set superscripts, although some specially designed glyphs keep the top of the numerator aligned with the top of the ...

  6. Tetration - Wikipedia

    en.wikipedia.org/wiki/Tetration

    5.2.2 Negative heights. 5.2.3 Real heights. ... it would be illogical to say "three raised to itself negative five times" or "four raised to itself one half of a time ...

  7. Modular exponentiation - Wikipedia

    en.wikipedia.org/wiki/Modular_exponentiation

    Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = b e mod m. From the definition of division, it follows that 0 ≤ c < m. For example, given b = 5, e = 3 and m = 13, dividing 5 3 = 125 by 13 leaves a remainder of c = 8.

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  9. Negative base - Wikipedia

    en.wikipedia.org/wiki/Negative_base

    A negative base (or negative radix) may be used to construct a non-standard positional numeral system.Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base b is equal to −r for some natural number r (r ≥ 2).