Based on a set of constructed integers,this paper uses the minimum number principle to use the problem of the method of summation in the quotient and remainder derived from the theorem of division algorithm,for solving the minimum value point and minimum value.

In this paper, by means of the division algorithm and congruence, firstly we discuss the fractions with the simplest decimal expansions; secondly, without having to carry out the actual calculation of the decimal, we discuss the length of the repeating part of the periodic decimal of 1/n and come to the corresponding conclusions.

Then the division formula with remainder is intuitively proved and applied.

According to the complexity of decoding circuit in digital TV and the moderate speed of decoding,a modified Euclidean algorithm is proposed based on the related deduction of division with reminder of polynomials.

The proposed algorithm use the related deduction of division with reminder of polynomials and the key equation is solved by column transformation of matrix.

According to the disadvantages of the complexity of decoding circuit in digital TV and the moderate speed of decoding,a modified Euclidean algorithm is proposed by the related deduction of division with reminder of polynomials.

To solve the rectangles cutting stock problem,this paper proposes a new algorithm-the smallest offcut deletion algorithm based on analyzing the main disadvantage of the traditional approximate algorithm.