Question Number 5749 by FilupSmith last updated on 26/May/16
$$\mathrm{if}\:{a}\equiv{b}\left(\mathrm{mod}\:{c}\right) \\ $$$${does}: \\ $$$${b}\equiv{a}\left(\mathrm{mod}\:{c}\right) \\ $$$$??? \\ $$
Commented by Rasheed Soomro last updated on 26/May/16
$$\mathrm{Of}\:\mathrm{course}. \\ $$$$\mathrm{If}\:\:\mathrm{m}\:\mid\:{p}\:,\mathrm{so}\:\mathrm{m}\:\mid\:−{p} \\ $$$$\mathrm{If}\:\mathrm{c}\:\mid\:\left({a}−{b}\right),\:\mathrm{then}\:\mathrm{c}\:\mid\:\left({b}−{a}\right)\: \\ $$
Commented by FilupSmith last updated on 26/May/16
$$\mathrm{hmm}.\:\mathrm{I}\:{think}\:\mathrm{I}\:\mathrm{understand}. \\ $$$$\mathrm{I}\:\mathrm{am}\:\mathrm{having}\:\mathrm{a}\:\mathrm{hard}\:\mathrm{time}\:\mathrm{teaching} \\ $$$$\mathrm{myself}\:\mathrm{modulus} \\ $$$$ \\ $$$$\mathrm{thank}\:\mathrm{you}!! \\ $$