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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.
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 ...
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 .
Poisson's summation formula appears in Ramanujan's notebooks and can be used to prove some of his formulas, in particular it can be used to prove one of the formulas in Ramanujan's first letter to Hardy. [clarification needed] It can be used to calculate the quadratic Gauss sum.
Some of the biggest brands in America, including Amazon, Meta, Walmart and McDonald’s, have recently changed or ended their diversity, equity and inclusion (DEI) programs. But e.l.f. Beauty, a ...
ALAMO, N.M. (Reuters) - - Twenty-eight-year old Ambrose Begay died after a fentanyl overdose under a tree 125 yards from his home on the Alamo Navajo reservation in southern New Mexico two years ago.
It is the second positive integer which can be expressed as the sum of two positive cubes in two different ways. The first such number, 1729 , is called the " Ramanujan–Hardy number ". 4104 is the sum of 4096 + 8 (that is, 16 3 + 2 3 ), and also the sum of 3375 + 729 (that is, 15 3 + 9 3 ).
Bowman's attorneys concerned about execution drug, racial bias. Bowman's attorneys are arguing that there's a "veil of secrecy" surrounding pentobarbital, the execution drug being used to kill him.