Let a = 1259 and b be an integer that is relatively prime to a. Every solution of the linear Diophantine equation ax+by=996b is of the form x = xo + ck, y=yo+dk, kez where c, d are certain integers and x = 0, y = yo is a particular integer solution. Assuming that d is a positive integer, what is the value of d? Enter O if there is not enough information to determine the value of d or if the Diophantine equation does not have any solutions.

Let a = 1259 and b be an integer that is relatively prime to a. Every solution of the linear Diophantine equation ax+by=996b is of the form x = xo + ck, y=yo+dk, kez where c, d are certain integers and x = 0, y = yo is a particular integer solution. Assuming that d is a positive integer, what is the value of d? Enter O if there is not enough information to determine the value of d or if the Diophantine equation does not have any solutions.

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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covered topics

prime numbers
linear Diophantine equations
systems of linear Diophantine equations.

Let a = 1259 and b be an integer that is relatively prime to a. Every solution of the linear Diophantine equation
ax + by 996b
is of the form
x = xo + ck,
y = yo + dk,
KEZ
where c, d are certain integers and x= xo, y = yo is a particular integer solution. Assuming that d is a positive integer, what is the value of d? Enter O if there is not enough
information to determine the value of d or if the Diophantine equation does not have any solutions.

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