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  2. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    For instance, the first counterexample must be odd because f(2n) = n, smaller than 2n; and it must be 3 mod 4 because f 2 (4n + 1) = 3n + 1, smaller than 4n + 1. For each starting value a which is not a counterexample to the Collatz conjecture, there is a k for which such an inequality holds, so checking the Collatz conjecture for one starting ...

  3. Goldbach's conjecture - Wikipedia

    en.wikipedia.org/wiki/Goldbach's_conjecture

    Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers. The conjecture has been shown to hold for all integers less than 4 × 10 18 but remains unproven despite considerable effort.

  4. Ages of Three Children puzzle - Wikipedia

    en.wikipedia.org/wiki/Ages_of_Three_Children_puzzle

    The Ages of Three Children puzzle (sometimes referred to as the Census-Taker Problem[1]) is a logical puzzle in number theory which on first inspection seems to have insufficient information to solve. However, with closer examination and persistence by the solver, the question reveals its hidden mathematical clues, especially when the solver ...

  5. Diophantine equation - Wikipedia

    en.wikipedia.org/wiki/Diophantine_equation

    In the following Diophantine equations, w, x, y, and z are the unknowns and the other letters are given constants: a x + b y = c {\displaystyle ax+by=c} This is a linear Diophantine equation or Bézout's identity. w 3 + x 3 = y 3 + z 3 {\displaystyle w^ {3}+x^ {3}=y^ {3}+z^ {3}} The smallest nontrivial solution in positive integers is 123 + 13 ...

  6. Word problem (mathematics education) - Wikipedia

    en.wikipedia.org/wiki/Word_problem_(mathematics...

    Word problem (mathematics education) In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation. As most word problems involve a narrative of some sort, they are ...

  7. Sum and Product Puzzle - Wikipedia

    en.wikipedia.org/wiki/Sum_and_Product_Puzzle

    The first solution with no prime number is the fourth which appears at X + Y ≤ 2522 or higher with values X = 16 = 2·2·2·2 and Y = 111 = 3·37. If the condition Y > X > 1 is changed to Y > X > 2, there is a unique solution for thresholds X + Y ≤ t for 124 < t < 5045, after which there are multiple solutions. At 124 and below, there are ...

  8. Word problem (mathematics) - Wikipedia

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

    Word problem (mathematics) Decision problem pertaining to equivalence of expressions. In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.

  9. Archimedes's cattle problem - Wikipedia

    en.wikipedia.org/wiki/Archimedes's_cattle_problem

    Archimedes's cattle problem. Archimedes's cattle problem (or the problema bovinum or problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions. Attributed to Archimedes, the problem involves computing the number of cattle in a herd of the sun god from a given set of restrictions.

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