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  2. Method of successive substitution - Wikipedia

    en.wikipedia.org/wiki/Method_of_successive...

    PROCEDURE. 1. Begin by rewriting the first congruence as an equation: x = 2a + 1, ∀a ∈ Z. 2. Rewrite the second congruence as an equation, and set the equation found in the first step equal to this equation, since x will substitute the x in the second congruence: x ≡ 2 (mod 3) x = 2a + 1 ≡ 2 (mod 3) 2a ≡ 1 (mod 3)

  3. Modular arithmetic - Wikipedia

    en.wikipedia.org/wiki/Modular_arithmetic

    Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...

  4. Quadratic reciprocity - Wikipedia

    en.wikipedia.org/wiki/Quadratic_reciprocity

    Quadratic Reciprocity (Legendre's statement). If p or q are congruent to 1 modulo 4, then: is solvable if and only if is solvable. If p and q are congruent to 3 modulo 4, then: is solvable if and only if is not solvable. The last is immediately equivalent to the modern form stated in the introduction above.

  5. International scale of river difficulty - Wikipedia

    en.wikipedia.org/wiki/International_scale_of...

    Because of the large range of difficulty that exists beyond Class IV, Class V is an open-ended, multiple-level scale designated by class 5.0, 5.1, 5.2, etc. Each of these levels is an order of magnitude more difficult than the last. That is, going from Class 5.0 to Class 5.1 is a similar order of magnitude as increasing from Class IV to Class 5.0.

  6. 2-6-6-4 - Wikipedia

    en.wikipedia.org/wiki/2-6-6-4

    The final class of 2-6-6-4s was the Norfolk and Western Railway's A class, built starting in 1936. 43 were built until 1950 but were operated until 1959 to prepare the ending of steam power. The powerful 2-6-6-4s were capable of more than 5,000 drawbar horsepower at 45 mph (72 km/h) and could reach 70 mph (110 km/h), while pulling heavy coal ...

  7. Reading - Wikipedia

    en.wikipedia.org/wiki/Reading

    Reading is the process of taking in the sense or meaning of letters, symbols, etc., especially by sight or touch. [1] [2] [3] [4]For educators and researchers, reading is a multifaceted process involving such areas as word recognition, orthography (spelling), alphabetics, phonics, phonemic awareness, vocabulary, comprehension, fluency, and motivation.

  8. 4-6-2+2-6-4 - Wikipedia

    en.wikipedia.org/wiki/4-6-2+2-6-4

    Evolved from. 2-6-2+2-6-2. Under the Whyte notation for the classification of steam locomotives by wheel arrangement, a 4-6-2+2-6-4 is a Garratt or Union Garratt articulated locomotive using a pair of 4-6-2 engine units back to back, with the boiler and cab suspended between them. The 4-6-2 wheel arrangement of each engine unit has four leading ...

  9. 2-6-4 - Wikipedia

    en.wikipedia.org/wiki/2-6-4

    The first engines of the class were modified 2-6-2 Prairie locomotives which were equipped with two-axle trailing bogies. In 1902, more were placed in service, but built with the 2-6-4 wheel arrangement. The latter were the first known tender locomotives in the world to be built with this wheel arrangement. [1] [2] [3]

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