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The origin of the class of such problems has been attributed to the Indian mathematician Mahāvīra in chapter VI, § 131 1 ⁄ 2, 132 1 ⁄ 2 of his Ganita-sara-sangraha (“Compendium of the Essence of Mathematics”), circa 850CE, which dealt with serial division of fruit and flowers with specified remainders. [1]
Change of variables is an operation that is related to substitution. However these are different operations, as can be seen when considering differentiation or integration (integration by substitution). A very simple example of a useful variable change can be seen in the problem of finding the roots of the sixth-degree polynomial:
The identity substitution, which maps every variable to itself, is the neutral element of substitution composition. A substitution σ is called idempotent if σσ = σ, and hence tσσ = tσ for every term t. When x i ≠t i for all i, the substitution { x 1 ↦ t 1, …, x k ↦ t k} is idempotent if and only if none of the variables x i ...
Often there are small stories, intriguing problems, and surprising results, which encourage discussions with friends and family. It had over 6 million participants from 57 countries in 2014. [ 1 ] In 2022, it has 84 participants countries and claims to be the largest competition for school students in the world.
In mathematics, an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. [1] A missing solution is a valid one which is lost during the solution process.
A mother named Tiesha Sanders recently took to Facebook to share her first-grader’s homework problem ... this is 1st grade math,” the caption read. The problem required the student to split ...
The odd friend may be less than the even one, as in 84729645 and 155315394 (abundancy of 896/351), or in 6517665, 14705145 and 2746713837618 (abundancy of 64/27). A square number can be friendly, for instance both 693479556 (the square of 26334) and 8640 have abundancy 127/36 (this example is credited to Dean Hickerson).
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