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2. Kuṭṭaka - Wikipedia

   en.wikipedia.org/wiki/Kuṭṭaka

   If c is not divisible by ⁠ (,) ⁠ then there are no integer solutions to this equation. After the division, we get the equation ⁠ ′ ′ = ′ ⁠. The solution to this equation is the solution to ⁠ = ⁠. Without loss of generality, let us consider a > b. Using Euclidean division, follow these recursive steps: a ′ = a 1 b ′ + r 1 b ...

3. Extraneous and missing solutions - Wikipedia

   en.wikipedia.org/wiki/Extraneous_and_missing...

   Because of this, often, the only simple effective way to deal with multiplication by expressions involving variables is to substitute each of the solutions obtained into the original equation and confirm that this yields a valid equation. After discarding solutions that yield an invalid equation, we will have the correct set of solutions.

4. Division (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Division_(mathematics)

   In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of b by a (written a \ b) is typically defined as the solution x to the equation a ∗ x = b, if this exists and is unique. Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b ...

5. Division algebra - Wikipedia

   en.wikipedia.org/wiki/Division_algebra

   Over an algebraically closed field K (for example the complex numbers C), there are no finite-dimensional associative division algebras, except K itself. [2] Associative division algebras have no nonzero zero divisors. A finite-dimensional unital associative algebra (over any field) is a division algebra if and only if it has no nonzero zero ...

6. Division algorithm - Wikipedia

   en.wikipedia.org/wiki/Division_algorithm

   Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.

7. Finite difference method - Wikipedia

   en.wikipedia.org/wiki/Finite_difference_method

   For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).

8. Separation of variables - Wikipedia

   en.wikipedia.org/wiki/Separation_of_variables

   This equation is an equation only of y'' and y', meaning it is reducible to the general form described above and is, therefore, separable. Since it is a second-order separable equation, collect all x variables on one side and all y' variables on the other to get: (′) (′) =.

9. Polynomial long division - Wikipedia

   en.wikipedia.org/wiki/Polynomial_long_division

   Polynomial long division can be used to find the equation of the line that is tangent to the graph of the function defined by the polynomial P(x) at a particular point x = r. [3] If R ( x ) is the remainder of the division of P ( x ) by ( x – r ) 2 , then the equation of the tangent line at x = r to the graph of the function y = P ( x ) is y ...