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  2. Fermat pseudoprime - Wikipedia

    en.wikipedia.org/wiki/Fermat_pseudoprime

    Starting at 17·257, the product of consecutive Fermat numbers is a base-2 pseudoprime, and so are all Fermat composites and Mersenne composites. The probability of a composite number n passing the Fermat test approaches zero for n → ∞ {\displaystyle n\to \infty } .

  3. Product (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Product_(mathematics)

    In set theory, a Cartesian product is a mathematical operation which returns a set (or product set) from multiple sets. That is, for sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) —where a ∈ A and b ∈ B. [5] The class of all things (of a given type) that have Cartesian products is called a Cartesian ...

  4. Direct product - Wikipedia

    en.wikipedia.org/wiki/Direct_product

    The direct sum and direct product are not isomorphic for infinite indices, where the elements of a direct sum are zero for all but for a finite number of entries. They are dual in the sense of category theory : the direct sum is the coproduct , while the direct product is the product.

  5. Sum-product number - Wikipedia

    en.wikipedia.org/wiki/Sum-product_number

    The natural numbers 0 and 1 are trivial sum-product numbers for all , and all other sum-product numbers are nontrivial sum-product numbers. For example, the number 144 in base 10 is a sum-product number, because 1 + 4 + 4 = 9 {\displaystyle 1+4+4=9} , 1 × 4 × 4 = 16 {\displaystyle 1\times 4\times 4=16} , and 9 × 16 = 144 {\displaystyle 9 ...

  6. Algebraic data type - Wikipedia

    en.wikipedia.org/wiki/Algebraic_data_type

    A general algebraic data type is a possibly recursive sum type of product types. Each constructor tags a product type to separate it from others, or if there is only one constructor, the data type is a product type. Further, the parameter types of a constructor are the factors of the product type.

  7. Addition - Wikipedia

    en.wikipedia.org/wiki/Addition

    The equivalence class of (a, b) contains either (a – b, 0) if a ≥ b, or (0, b – a) otherwise. If n is a natural number, one can denote +n the equivalence class of (n, 0), and by –n the equivalence class of (0, n). This allows identifying the natural number n with the equivalence class +n. Addition of ordered pairs is done component-wise:

  8. Telescoping series - Wikipedia

    en.wikipedia.org/wiki/Telescoping_series

    A telescoping product is a finite product (or the partial product of an infinite product) that can be canceled by the method of quotients to be eventually only a finite number of factors. [ 7 ] [ 8 ] It is the finite products in which consecutive terms cancel denominator with numerator, leaving only the initial and final terms.

  9. Erdős–Szemerédi theorem - Wikipedia

    en.wikipedia.org/wiki/Erdős–Szemerédi_theorem

    The sum-product conjecture informally says that one of the sum set or the product set of any set must be nearly as large as possible. It was originally conjectured by Erdős in 1974 to hold whether A is a set of integers, reals, or complex numbers. [3] More precisely, it proposes that, for any set A ⊂ ℂ, one has

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