Leo Liu
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Could someone explain why ##[a][x_0]=[c]\iff ax_0\equiv c\, (mod\, m)##?
My instructor said it came from the definition of congruence class. But I am not convinced.
[Congruence class] Proof of modular arithmetic theorem
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Could someone explain why ##[a][x_0]=[c]\iff ax_0\equiv c\, (mod\, m)##?
My instructor said it came from the definition of congruence class. But I am not convinced.
Recall that ##[x] = [y]## if ##x \equiv y \ (\mathrm{mod \ m})##. Then it's just a case of using ##[a][x_0] = [ax_0]##.
Leo Liu
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Wonderful. I didn't know this form of definition but after seeing its justification (transitivity and symmetry) I am convinced.ergospherical said: