In this situation the teacher is faced with a dilemma --the focus of the lesson is on

square numbers, and examining what constitutes a number would require substantial deviation from the original intention of the lesson.

In this section, the proposed scheme is described in three parts: the new quantization range table is based on the perfect

square number, embedding procedure, and extraction procedure.

This classification system proved interesting because of its connection to the existing "

square numbers" pattern.

Explaining the relationship between the new number of stairs and the next

square number also proved to be difficult for the students, with several expressing confusion.

If positive integer n is a square-free number (That is, for any prime p, if p | n, then [P.sup.2] [??] n), then [a.sub.n] is not a complete

square number.

The relevant content description is taken from Year 7 of the Australian Curriculum: Mathematics, in which students "Investigate index notation and represent whole numbers as products of powers of prime numbers" (ACMNA149) and "Investigate and use square roots of perfect

square numbers" (ACMNA150).

In reference [2], Professor F.Smarandache asked us to study such a problem: How many perfect

square number are there in the sequence {a(n)I and {b(n)j?

The sum of the numbers assigned to the students in each pair must be a

square number.

This example illustrates that a link could be forged between the line number and the number of consecutive odd integers in each equation, as well as the

square number on the right side of the equation.

That is, a(n) is the smallest positive integer such that na(n) is a perfect

square number. In this paper, we use the analytic method to study the number of the solutions of the equation involving the square complements, and obtain its all solutions of this equation.

which is the relationship between succeessive triangular numbers and a

square number. If we write this out for the first six values of k we have

I have also seen students work together in small groups with calculators to discover if a thousand is a

square number and can be created through a grid pattern rather than individual pieces.