Counting Natural and Integer Solutions to Equations and Inequalities

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-7
Year of Publication : 2021
Authors : Aleksa Srdanov, Dragan Stojiljkovic
  10.14445/22315373/IJMTT-V67I7P503

MLA

MLA Style: Aleksa Srdanov, Dragan Stojiljkovic "Counting Natural and Integer Solutions to Equations and Inequalities" International Journal of Mathematics Trends and Technology 67.7 (2021):21-25. 

APA Style: Aleksa Srdanov, Dragan Stojiljkovic(2021). Counting Natural and Integer Solutions to Equations and Inequalities International Journal of Mathematics Trends and Technology, 21-25.

Abstract
In this paper, formulas for the purpose of counting both natural number and integer solutions to linear equations and inequalities will be gradually derived using combinations with repetitions. General formulas will be derived and each solution will be additionally generalized.

Reference

[1] Fred Roberts, Barry Tesman, Fred S. Roberts., Applied Combinatorics (2nd Edition), (2021).
[2] Grimaldi R.P., Discrete and Combinatorial Mathematics, 5th edition ,(2005).
[3] M Hall, Combinatorial theory. Blaisdell, (1967).
[4] Aleksa Srdanov, The universal formulas for the number of partitions. , Proc. Indian Acad. Sci. (Math. Sci.), 128(40) (2018).
[5] Aleksa Srdanov, Fractal form of the partition functions p (n). AIMS Mathematics, 5(3) (2020) 2539-2568.
[6] Aleksa Srdanov, Invariants in partition classes. AIMS Mathematics, 5(6) (2020) 6233-6243.
[7] Aleksa Srdanov, One combinatorial problem, many solutions, Collection of papers, Tehnical college, Pozarevac 1 (2011).
[8] Rade Dacic, Elementary combinatorics, Mathematical institute, Belgrade, (1977).

Keywords : elementary combinatorics, combinations with repetitions.