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The monkey and the coconuts is the best known representative of a class of puzzle problems requiring integer solutions structured as recursive division or fractionating of some discretely divisible quantity, with or without remainders, and a final division into some number of equal parts, possibly with a remainder.
The Erdős–Straus conjecture is one of many conjectures by Erdős, and one of many unsolved problems in mathematics concerning Diophantine equations. Although a solution is not known for all values of n, infinitely many values in certain infinite arithmetic progressions have simple formulas for their solution, and skipping these known values ...
In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. [1][2] A more general definition includes all positive rational numbers with this property. [3] The sequence of (integer) congruent numbers starts with. For example, 5 is a congruent number because it is the area of ...
The lattice Con(A) of all congruence relations on an algebra A is algebraic. John M. Howie described how semigroup theory illustrates congruence relations in universal algebra: In a group a congruence is determined if we know a single congruence class, in particular if we know the normal subgroup which is the class containing the identity.
The audience for this book, according to reviewer Kevin Davis, is "mid-way between a specialised and a general readership". [8] Alex Criddle echoes this opinion, suggesting that "those without a special interest in mathematics may find it very dry and hard to understand" but that it should be read by "anyone interested in the history of mathematics, egyptology, or Egyptian culture". [7]
In mathematics, Ramanujan's congruences are the congruences for the partition function p (n) discovered by Srinivasa Ramanujan: In plain words, e.g., the first congruence means that If a number is 4 more than a multiple of 5, i.e. it is in the sequence. 4, 9, 14, 19, 24, 29, . . . then the number of its partitions is a multiple of 5.
Poincaré and the Three-Body Problem is a monograph in the history of mathematics on the work of Henri Poincaré on the three-body problem in celestial mechanics.It was written by June Barrow-Green, as a revision of her 1993 doctoral dissertation, and published in 1997 by the American Mathematical Society and London Mathematical Society as Volume 11 in their shared History of Mathematics ...
Cubic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x 3 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of the main theorem, which states that if p and q are primary numbers in the ring of Eisenstein integers, both coprime to 3, the congruence x 3 ≡ p (mod q) is solvable if and only if ...