# Solutions of Linear Diophantine Equation ax + by = c

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If (xo,yo) is a solution of the Linear Diophantine equation ax + by = c , then the set of solutions of the equation consists of all integer pairs (x,y), where either x = xo + tb/d and y = yo - ta/d ( t = ........,-2,-1,0,1,2,........)

or , x = xo - tb/d and y = yo + ta/d ( t = .........,-2,-1,0,1,2,.......) where d = g.c.d.(a,b).

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##### Solution Summary

This solution is comprised of a detailed explanation for the Linear Diophantine Equation.

It contains step-by-step explanation for if (xo,yo) is a solution of the Linear Diophantine equation ax + by = c ,

then the set of solutions of the equation consists of all integer pairs (x,y), where

either x = xo + tb/d and y = yo - ta/d ( t = ........,-2,-1,0,1,2,........)

or , x = xo - tb/d and y = yo + ta/d ( t = .........,-2,-1,0,1,2,.......) where d = g.c.d.(a,b).

Solution contains detailed step-by-step explanation.

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- BSc, Manipur University
- MSc, Kanpur University

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