Find the value of y in the mod 9 system.
5 x y = 4

Question

anonymous · Answer

5y=4 
y=4/5
what is mod 9 system if i may ask?

cruffo · Answer

$$5y=4 \;\text{mod(9)}$$ ???

anonymous · Answer

modular system with a specific number of elements are analogous to the 12 oclock system

cruffo · Answer

There is an algebraic way to solve these, but since there are only 9 elements, trial and error can also work.
5(1) = 5 mod(9)
5(2) = 10 = 1 mod(9)
5(3) = 15 = 6 mod(9)
5(4) = 20 = 2 mod(9)
5(5) = 25 = 7 mod(9)
5(6) = 30 = 3 mod(9)
5(7) = 35 = 8 mod(9)
5(8) = 40 = 4 (mod(9)  ------ solution y = 8

anonymous · Answer

made easier to understand you writing out...thx

anonymous · Answer

what is that?

anonymous · Answer

Modulo congruence

$$a \cong b (mod\ c) \implies \exists k \in Z\ |\ {a-b \over c} = k $$

cruffo · Answer

multiply, then divide the result by the indicated mod #, take the remainder.  Most likely studied in beginning number theory, or abstract algebra, or cryptography.

anonymous · Answer

Are you looking for solutions where 5y is congruent to 4 ? Or are you looking for solutions where 5y (mod 9) = 4?

anonymous · Answer

Actually those would be the same since 4 mod 9 is 4.

cruffo · Answer

:)  I was just gonna ask about that!