We search for rectangles with dimensions such that the expression is represented by 2-digit & 4-digit Jarasandha numbers. In the above expression , & denote the area and semi-perimeter of the rectangle respectively. Also, total number of rectangles, each satisfying the above relation is obtained.
Keywords: Rectangles, Jarasandha numbers.
1. Introduction
Mathematics is the language of patterns and relationships, and is used to describe anything that can be quantified. Number theory is one of the largest and oldest branches of mathematics. The main goal of number theory is to discover interesting and unexpected relationships. It is devoted primarily to the study of natural numbers and integers. In number theory, rectangles have
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For =6, all the rectangles are primitive.
For =8,10 One rectangle is non-primitive and the other is primitive.
11-24
1 For =11,13,15,16,17,19,21,22,23 the rectangle is non-primitive.
For =12,14,18,20,24 the rectangle is primitive.
Case 4:
Consider the 4-digit Jarasandha number 9801,
Applying the method of factorization, we have From the above values, the following results are observed:
Table 4:
Number of rectangles related to 9801
Observations
0 7 2 rectangles are primitive and the remaining 5 are non-primitive.
1, 2
6 For =1, all the rectangles are non-primitive.
For =2, all the rectangles are primitive.
3-8
5 For =3,5,6,7 all the rectangles are non-primitive.
For =4, One rectangle is non-primitive and the remaining 4 are primitive.
For =8, all the rectangles are primitive.
9, 10
4 For =9, all the rectangles are non-primitive.
For =10, all the rectangles are primitive.
11-26
3 For =11,13,15,17,19,21,23,25 all the rectangles are non-primitive.
For =12,18,24 One rectangle is primitive and the remaining 2 are non-primitive.
For =14, all the rectangles are primitive.
For =16,20,22,26 One rectangle is non-primitive and the remaining 2 are
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