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= d. The linear Diophantine equation ax + by = c has a solution if and only if d | c. Let xo, yo be any particular solution, that is, axo+byo = c. All other solutions are given by Let (a, b) b - (2) ₁. t. x = xo + y = Yo- (2) ₁ t where t is an arbitrary integer. (1.1)

= d. The linear Diophantine equation ax + by = c has a solution if and only if d | c. Let xo, yo be any particular solution, that is, axo+byo = c. All other solutions are given by Let (a, b) b - (2) ₁. t. x = xo + y = Yo- (2) ₁ t where t is an arbitrary integer. (1.1)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let (a, b) =d. The linear Diophantine equation ax + by = c has a solution if and only if dc. Let xo, yo be any particular solution, that is, axo+byo = c. All other solutions are given by x = xo + (2) + t, y = Yo - (²) t where t is an arbitrary integer. (1.1)
Transcribed Image Text:Let (a, b) =d. The linear Diophantine equation ax + by = c has a solution if and only if dc. Let xo, yo be any particular solution, that is, axo+byo = c. All other solutions are given by x = xo + (2) + t, y = Yo - (²) t where t is an arbitrary integer. (1.1)
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