Integral Solution of Linear Indeterminate Equations of n Variables:Generalized Matrix Kuttaka Method

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Authors

  • P. J. Sindhurani
     Department of Mathematics, Cochin University of Science and Technology Cochin 682022 ,IN
  • V. P. N. Nampoori
     International School of Photonics,Cochin University of Science and Technology, Cochin 682022 ,IN

DOI:

https://doi.org/10.24906/isc/2019/v33/i2/183892

Keywords:

Linear Indeterminate Equations, Sulbasutras, Kuttaka, Karanapadhati, Aryabhaá¹­iya, Generalized Matrix Kuttaka.

Abstract

Problems of indeterminate equations first appeared in Baudhayana Sulbasutra (800-500 B.C.). But a general method of integral solutions of linear indeterminate equations is not described in it, except some geometrical solutions. Aryabhata I (476 A.D.) first gave a general method (kuttaka) of integral solution of linear indeterminate equations of two variables. The kuttaka method was subsequently discussed with modifications by several ancient and medieval Indian mathematicians. However, a general method of solving indeterminate equations of n variables is not available in kuttaka method. The present paper reviews the method used by earlier writers, and describes kuá¹­á¹­aka in terms of matrices and determinants. Generalizing this matrix kuttaka method, we present a general method of integral solutions of linear indeterminate equations of n variables. Using this method, we can evaluate all positive integral solutions of the indeterminate equations in Sulbasutras (800-200 B.C.).

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Published

2019-03-01

How to Cite

Sindhurani, P. J., & Nampoori, V. P. N. (2019). Integral Solution of Linear Indeterminate Equations of n Variables:Generalized Matrix <i>Kuttaka</i> Method. Indian Science Cruiser, 33(2), 48–58. https://doi.org/10.24906/isc/2019/v33/i2/183892

Issue

Volume 33, Issue 2, March 2019

Section

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