[[Congruence]] How to solve for n. 5n≅4 (mod 3) and 8n≅3(mod 4) ??

Question

[[Congruence]]      How to solve for n.   5n≅4 (mod 3)      and 8n≅3(mod 4) ??

anonymous · Answer

≅  this stuff is  'three short dashed lines'.

anonymous · Answer

when 8n divide by 4 give remainder 0 !!!

anonymous · Answer

its impossible to have 8n≅3(mod 4)

lgbasallote · Answer

how i understand this:
5n≅4 (mod 3)  
solve for 4(mod 3) first

4(mod 3) = 1 because 4 divided by 3 has remainder 1

5n≅1
divide both sides by 5

n≅1/5

anonymous · Answer

@lyy1992 
am i right?

anonymous · Answer

i guess there is no solution for this one 5n≅4 (mod 3)  since the value of  5n(mod 3) are just 0,2,and 1.      as well as 8n≅3(mod 4), the value of 8n(mod 4) is just 0.      am i right? kinda confused...

anonymous · Answer

ur right~ @mukushla

anonymous · Answer

5n≅2n≅0,1,2 (mod 3) also impossible
so ther is no solution for n

anonymous · Answer

and yes u r right