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Question Number 5749 by FilupSmith last updated on 26/May/16

if a≡b(mod c) does: b≡a(mod c) ???

$$\mathrm{if}\:{a}\equiv{b}\left(\mathrm{mod}\:{c}\right) \\ $$$${does}: \\ $$$${b}\equiv{a}\left(\mathrm{mod}\:{c}\right) \\ $$$$??? \\ $$

Commented by Rasheed Soomro last updated on 26/May/16

Of course. If m ∣ p ,so m ∣ −p If c ∣ (a−b), then c ∣ (b−a)

$$\mathrm{Of}\:\mathrm{course}. \\ $$$$\mathrm{If}\:\:\mathrm{m}\:\mid\:{p}\:,\mathrm{so}\:\mathrm{m}\:\mid\:−{p} \\ $$$$\mathrm{If}\:\mathrm{c}\:\mid\:\left({a}−{b}\right),\:\mathrm{then}\:\mathrm{c}\:\mid\:\left({b}−{a}\right)\: \\ $$

Commented by FilupSmith last updated on 26/May/16

hmm. I think I understand. I am having a hard time teaching myself modulus thank you!!

$$\mathrm{hmm}.\:\mathrm{I}\:{think}\:\mathrm{I}\:\mathrm{understand}. \\ $$$$\mathrm{I}\:\mathrm{am}\:\mathrm{having}\:\mathrm{a}\:\mathrm{hard}\:\mathrm{time}\:\mathrm{teaching} \\ $$$$\mathrm{myself}\:\mathrm{modulus} \\ $$$$ \\ $$$$\mathrm{thank}\:\mathrm{you}!! \\ $$

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