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Congruence (symbol: ) is the state achieved by coming together, the state of agreement. The Latin congruō meaning “I meet together, I agree”. As an abstract term, congruence means similarity between objects. Congruence, as opposed to approximation, is a relation which implies a species of equivalence.


  • Congruence (geometry), being isometric — roughly, the same size and shape
  • Congruence or congruence relation, in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure
  • In modular arithmetic, having the same remainder when divided by a specified integer
    • Ramanujan's congruences, congruences for the partition function, p(n), first discovered by Ramanujan in 1919
    • Congruence subgroup, a subgroup defined by congruence conditions on the entries of a matrix group with integer entries
    • Congruence of squares, in number theory, a congruence commonly used in integer factorization algorithms
  • Congruence (manifolds), in the theory of smooth manifolds, the set of integral curves defined by a nonvanishing vector field defined on the manifold
  • Congruence (general relativity), in general relativity, a congruence in a four-dimensional Lorentzian manifold that is interpreted physically as a model of space time, or a bundle of world lines
  • Zeller's congruence, an algorithm to calculate the day of the week for any date
  • Scissors congruence, related to Hilbert's third problem


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