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Question Number 66815 by Rio Michael last updated on 20/Aug/19
solve the congruence equation     6x ≡ 4 (mod 5)  i need help please with some explanations
solvethecongruenceequation6x4(mod5)ineedhelppleasewithsomeexplanations
Commented by mathmax by abdo last updated on 20/Aug/19
if we consider congruence modulo 5  we have   6x ≡4 [5] ⇒6^− x^− =4^−     but 6^− =5^−  +1^− =1^−  and 4^− =(−1)^−  ⇒  x^− =−1[5] ⇒x+1 =5k   ⇒x =5k−1  with k ∈Z .
ifweconsidercongruencemodulo5wehaveMissing \left or extra \rightx=1[5]x+1=5kx=5k1withkZ.
Answered by Rasheed.Sindhi last updated on 20/Aug/19
6x≡4+4×5=24(mod 5)    x≡4(mod 5)
6x4+4×5=24(mod5)x4(mod5)
Answered by mr W last updated on 20/Aug/19
6x=5n+4=5(n−4)+24  x=((5(n−4))/6)+4  with n−4=6m  ⇒x=5m+4  i.e. x≡4(mod 5)
6x=5n+4=5(n4)+24x=5(n4)6+4withn4=6mx=5m+4i.e.x4(mod5)
Commented by Rio Michael last updated on 20/Aug/19
i still don′t undestand how these equations are solved
istilldontundestandhowtheseequationsaresolved
Commented by mr W last updated on 21/Aug/19
don′t you understand what  6x≡4 (mod 5) means or where is your  problem?
dontyouunderstandwhat6x4(mod5)meansorwhereisyourproblem?
Commented by Rio Michael last updated on 21/Aug/19
i think so sir,because am new to this further mathematics stuffs
ithinksosir,becauseamnewtothisfurthermathematicsstuffs
Commented by mr W last updated on 21/Aug/19
a≡b (mod c) means  when a and b are divided by c, they  have the same remainder.  in other word:  a=nc+b
ab(modc)meanswhenaandbaredividedbyc,theyhavethesameremainder.inotherword:a=nc+b
Commented by Rio Michael last updated on 25/Aug/19
thank you so much sir
thankyousomuchsir

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