Solving congruences and diophantine equations in number theory

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  • #1
Hello. I do not understand how to solve systems of three or two congruences of one unknown of first order, a congruence of one unknown of second order and a system of diophantine equations of two or three unknowns. Could someone help me by providing examples in these cases? Thank you.
 

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  • #2
Office_Shredder
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Why don't you post an example of an equation and what you don't understand about how to solve it
 
  • #3
Solve the system 8x ≡ 4(mod20), 15x ≡ 10(mod35), 9x ≡ 12(mod39). As well, if you can tell me how to apply it to other similar situations. Find also the solutions of the system x ≡ 1(mod15), x ≡ 7(mod18). Thank you.
 
  • #4
hutchphd
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I enjoy systems of equations such as these. They remind me of a multifaceted gem.
 
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