Suppose that the system of linear Diophantine equations has solutions of the form x + 5y + 2z = 158 9y-z = 247 x = xo + Ak, y=yo+Bk, z = zo + CK, for some integer constants A, B, C. Find the smallest positive value of x among all of the solutions. KEZ

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Need help with this Intro to Elementary Number Theory homework problem.

 

covered topics

  • prime numbers
  • linear Diophantine equations
  • systems of linear Diophantine equations.

 

Suppose that the system of linear Diophantine equations
has solutions of the form
x + 5y + 2z = 158
9yz = 247
x = xo + Ak, y = yo + Bk, 2 = 20 + Ck, kez
for some integer constants A, B, C. Find the smallest positive value of x among all of the solutions.
Transcribed Image Text:Suppose that the system of linear Diophantine equations has solutions of the form x + 5y + 2z = 158 9yz = 247 x = xo + Ak, y = yo + Bk, 2 = 20 + Ck, kez for some integer constants A, B, C. Find the smallest positive value of x among all of the solutions.
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