On the number of solutions of the Diophantine equation of Frobenius - General case

Komatsu, T.

Mathematical Communications, Vol. 8 No. 2, 2003.

Original scientific paper

On the number of solutions of the Diophantine equation of Frobenius - General case

T. Komatsu

Full text: english pdf 150 Kb

page 195-206

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APA 6th Edition

Komatsu, T. (2003). On the number of solutions of the Diophantine equation of Frobenius - General case. Mathematical Communications, 8 (2), 195-206. Retrieved from https://hrcak.srce.hr/730

MLA 8th Edition

Komatsu, T.. "On the number of solutions of the Diophantine equation of Frobenius - General case." Mathematical Communications, vol. 8, no. 2, 2003, pp. 195-206. https://hrcak.srce.hr/730. Accessed 11 Apr. 2025.

Chicago 17th Edition

Komatsu, T.. "On the number of solutions of the Diophantine equation of Frobenius - General case." Mathematical Communications 8, no. 2 (2003): 195-206. https://hrcak.srce.hr/730

Harvard

Komatsu, T. (2003). 'On the number of solutions of the Diophantine equation of Frobenius - General case', Mathematical Communications, 8(2), pp. 195-206. Available at: https://hrcak.srce.hr/730 (Accessed 11 April 2025)

Vancouver

Komatsu T. On the number of solutions of the Diophantine equation of Frobenius - General case. Mathematical Communications [Internet]. 2003 [cited 2025 April 11];8(2):195-206. Available from: https://hrcak.srce.hr/730

IEEE

T. Komatsu, "On the number of solutions of the Diophantine equation of Frobenius - General case", Mathematical Communications, vol.8, no. 2, pp. 195-206, 2003. [Online]. Available: https://hrcak.srce.hr/730. [Accessed: 11 April 2025]

Abstract

We determine the number of solutions of the equation $a_{1} x_{1} + a_{2} x_{2} + \dots + a_{m} x_{m} = b$ in non-negative integers $x_{1}$ , $x_{2}$ ,
$\dots$ , $x_{n}$ . If $m = 2$ , then the largest $b$ for which no
solution exists is $a_{1} a_{2} - a_{1} - a_{2}$ , and an explicit formula for
the number of solutions is known. In this paper we give the method
for computing the desired number. The method is illustrated with
several examples.

Keywords

Diophantine problem of Frobenius; number of solutions

Hrčak ID:

730

URI

https://hrcak.srce.hr/730

Publication date:

22.12.2003.

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Mathematical Communications, Vol. 8 No. 2, 2003.

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