Abstract

This study involves the study of the long-term behaviors of rainfall as it is affected by changes to forest area and the rise in global temperature. Global temperature and forest cover are considered annually while the amount of rainfall are considered seasonally to best capture the effects of severe weather hazards such as drought and puberty. A differential equation model was developed and verified using the mean global temperature annually, forest area, the daily amounts of rainfall. The rise in global temperature as well as the decline in forest area can be, as shown in the seminar, represented by logistic equations. Rainfall is, however, represented as a periodic function; hence, second order differential equation, of which the solution is periodic, is used to represent the rate of change in the amount of rainfall. In addition, by correlation analysis, the predator-prey terms of forest, global temperature and rainfall are presented in the models. DOI : 10.7176/MTM/9-1-03

Highlights

  • In this paper we deal with divisibility criteria for any integer in decimal system

  • Are some facts of congruence theory,which is an important tool in number theory, besides handling related problems as solving congruence equations, remainder problems and the like, it is being used in the development of a generalized test of divisibility

  • The basic facts that are to be used in this paper are linear congruences and their properties along with modular Arthmetics and the Fundamental theorem of Arthmetics

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Summary

Congruence

If a and b are integers; the notation a≡ (modm) (“ais congruent to bmod m") means that a and b share the same remainder with respect to integer division by m, or, equivalently, that m|b−a. The condition m|b−a can be expressed as b=a+mq for some integer q.a is congruent to b mod m precisely if the difference of a and b is a multiple of m.An observation that will be useful later is that a≡(amodm)(modm).

Properties of Congruence
GCD-Theorem
Special divisibility criteria for integers coprime to 10
Special divisibility criteria for integers not coprime to 10

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