THE LINEAR INDETERMINATE EQUATION - A BRIEF HISTORICAL ACCOUNT

Abstract

The paper presents in brief the contribution of Aryabhata in developing general solution of indeterminate equation of the type ax + c = by, where a, b, c are the integers. Also the contributions of Bhaskara and Brahmagupta in developing the solution of the indeterminate equations are discussed. Finally an example of Paramesvara is illustrated to solve coupled linear indeterminate equations which may be adopted to find the multiplicative inverse in a group that is of interest in cryptology, signal processing, coding and computer design.

Keywords

• Indeterminate equation
• Chinese remainder theorem
• Aryabhata
• Kuttaka
• Brahmagupta
• Bhaskara