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2. Ramanujan's sum - Wikipedia

   en.wikipedia.org/wiki/Ramanujan's_sum

   In number theory, Ramanujan's sum, usually denoted c q (n), is a function of two positive integer variables q and n defined by the formula = (,) =,where (a, q) = 1 means that a only takes on values coprime to q.

3. Partition function (number theory) - Wikipedia

   en.wikipedia.org/wiki/Partition_function_(number...

   The multiplicative inverse of its generating function is the Euler function; by Euler's pentagonal number theorem this function is an alternating sum of pentagonal number powers of its argument. Srinivasa Ramanujan first discovered that the partition function has nontrivial patterns in modular arithmetic, now known as Ramanujan's congruences.

4. Srinivasa Ramanujan - Wikipedia

   en.wikipedia.org/wiki/Srinivasa_Ramanujan

   Srinivasa Ramanujan Aiyangar [a] (22 December 1887 – 26 April 1920) was an Indian mathematician.Often regarded as one of the greatest mathematicians of all time, though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then ...

5. Taxicab number - Wikipedia

   en.wikipedia.org/wiki/Taxicab_number

   Srinivasa Ramanujan (picture) was bedridden when he developed the idea of taxicab numbers, according to an anecdote from G. H. Hardy.. In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. [1]

6. Ramanujan sum - Wikipedia

   en.wikipedia.org/?title=Ramanujan_sum&redirect=no

   Download as PDF; Printable version; From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Ramanujan's sum; Retrieved from " ...

7. Rogers–Ramanujan continued fraction - Wikipedia

   en.wikipedia.org/wiki/Rogers–Ramanujan...

   The Rogers–Ramanujan continued fraction is a continued fraction discovered by Rogers (1894) and independently by Srinivasa Ramanujan, and closely related to the Rogers–Ramanujan identities. It can be evaluated explicitly for a broad class of values of its argument.

8. Ramanujan–Sato series - Wikipedia

   en.wikipedia.org/wiki/Ramanujan–Sato_series

   Ramanujan made the enigmatic remark that there were "corresponding theories", but it was only in 2012 that H. H. Chan and S. Cooper found a general approach that used the underlying modular congruence subgroup (), [3] while G. Almkvist has experimentally found numerous other examples also with a general method using differential operators.

9. Elementary Number Theory, Group Theory and Ramanujan Graphs

   en.wikipedia.org/wiki/Elementary_Number_Theory...

   Its authors have divided Elementary Number Theory, Group Theory and Ramanujan Graphs into four chapters. The first of these provides background in graph theory, including material on the girth of graphs (the length of the shortest cycle), on graph coloring, and on the use of the probabilistic method to prove the existence of graphs for which both the girth and the number of colors needed are ...