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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The solution = is in fact a valid solution to the original equation; but the other solution, =, has disappeared. The problem is that we divided both sides by x {\displaystyle x} , which involves the indeterminate operation of dividing by zero when x = 0. {\displaystyle x=0.}
This is an accepted version of this page This is the latest accepted revision, reviewed on 17 January 2025. Civil services examination in India This article is about the examination in India. For civil service examinations in general, see civil service entrance examination. This article may need to be rewritten to comply with Wikipedia's quality standards. You can help. The talk page may ...
He then used this lemma to both generate infinitely many (integral) solutions of Pell's equation, given one solution, and state the following theorem: Theorem (Brahmagupta): If the equation x 2 − N y 2 = k {\displaystyle \ x^{2}-Ny^{2}=k} has an integer solution for any one of k = ± 4 , ± 2 , − 1 {\displaystyle \ k=\pm 4,\pm 2,-1} then ...
When seeking a solution, one or more variables are designated as unknowns. A solution is an assignment of values to the unknown variables that makes the equality in the equation true. In other words, a solution is a value or a collection of values (one for each unknown) such that, when substituted for the unknowns, the equation becomes an equality.
There are a total of 180 questions asked in the exam, 45 questions each from Physics, Chemistry, Botany and Zoology. Each correct response fetches 4 marks and each incorrect response gets -1 negative marking. The exam duration is 3 hours (180 min). The exam is of 720 marks (maximum marks).
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
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 ...