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  1. Hace 5 días · Ramanujan's sum. In number theory, Ramanujan's sum, usually denoted cq ( 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 mentioned the sums in a 1918 paper. [1]

  2. Hace 4 días · Recently, a student have asked a question involving the expression $$ \sum_{n=0}^{\infty} (-1)^n (4n+1) \frac{(2n-1)!!}{(2n)!!} $$ He (the student) couldn't recall ...

  3. Hace 5 días · Because it is the smallest number expressible as the sum of two positive cubes in two different ways. Note: The smallest such number is 1729. As we can represent it in two different ways as a sum of two cubes. It is given by: 1729 = 13 +123 = 93 + 103 1729 = 1 3 + 12 3 = 9 3 + 10 3.

  4. en.wikipedia.org › wiki › RamayanaRamayana - Wikipedia

    Hace 2 días · Ramayana series by Ashok Banker. A fictional retelling of the Ramayana. It has eight books — Prince of Ayodhya, Siege of Mithila, Demons of Chitrakut, Armies of Hanuman, Bridge of Rama, King of Ayodhya, Vengeance of Ravana and Sons of Sita. Rama Chandra Series by Amish Tripathi, a fictional retelling of the Ramayana.

  5. Hace 4 días · The Ramanujan Journal - We introduce a certain discrete probability distribution $$P_{n,m,k,l;q}$$ having non-negative integer parameters n, m, k, l and quantum parameter...

  6. Hace 3 días · Additionally, the number 1729 is known as the Hardy-Ramanujan number, named after a famous mathematician who stated that it was rather a dull number after being assigned a cab with this number. This seemingly ordinary number later became famous in mathematics as it is the smallest number expressible as the sum of two different cubes in two different ways.

  7. Samuel Adams, one of the leading figures of the American Revolution, wrote this document in 1772 to assert the natural and constitutional rights of the colonists against British oppression. He argued that the colonists had the same rights as Englishmen, and that they should resist any attempts to violate them. This document is a valuable source for understanding the political philosophy and ...