If seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder. Also, if three times the larger number is divided by the smaller one, we get 4 as quotient and 3 as remainder. Find the numbers.

A division algorithm is a rule that calculates the quotient and remainder of two integers, N and D, using Euclidean division. It can be applied by hand or used in software and digital circuit designs.  The division algorithm states that for any integer, a, and any positive integer, b, there are unique integers q and r such that a = bq + r. In this equation, r is greater than or equal to 0 and less than b.  The division algorithm can also be applied to polynomials.  The division algorithm for polynomials states that:  f(x) = q(x) g(x) + r(x)  This is the same as:  Dividend = Divisor *... Show more

A division algorithm is a rule that calculates the quotient and remainder of two integers, N and D, using Euclidean division. It can be applied by hand or used in software and digital circuit designs. 

The division algorithm states that for any integer, a, and any positive integer, b, there are unique integers q and r such that a = bq + r. In this equation, r is greater than or equal to 0 and less than b. 
The division algorithm can also be applied to polynomials. 

The division algorithm for polynomials states that: 
f(x) = q(x) g(x) + r(x) 
This is the same as:  Dividend = Divisor * Quotient + Remainder 

Here, r(x) is the remainder polynomial and is equal to 0 and degree r(x) < degree g(x). 
For example, the division algorithm can be used to find the other two zeros of a polynomial if one of the zeros is known.

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