So this is the question, there was a explaination from greg but I used a different approach
I tried to take out 9 and and when divided by 6 , it will be simplified to 3/2 multiplied by the sum in the bracket, and when focusing with the units digit as I did I am getting the remainder as 1, no idea what am I doing wrong, can someone help me understand what am I doin wrong here?
You don’t consider the unit places for anything other than if you’re finding the remainder when dividing by 10, so everything below the third line is unfounded.
Also the second line simplification isn’t warranted cuz like you aren’t dividing the sum by 6 but rather trying to find the remainder modulo 6. For example, 10/4 doesn’t have the same remainder as 5/2, right?
Essentially, such simplifications are a bit fishy, so you shouldn’t ever do them unless you know where you’re headed.
To solve your actual problem, if you can show that 3^k when divided by 6 always leaves a remainder of 3 (for appropriate k ofc) then you’re done. In which case, you’ve boiled your question down to finding the remainder of 3 \cdot 9 when divided by 6, which is obviously just 3. I skipped a bit of steps, so that you can attempt it yourself (if u wish) to make sense of what i said.
Is the correct answer B, 3?
just making sure…
anyways, for remainders we only look at unit digits. The pattern for unit digits for powers of 9 repeat in the pattern of 9,1,9,1, etc.
so ud for 9^1…9^9 = 9+1+9+1+9+1+9+1+9 = 49
which essentially is 9 since we only care about the ud
9 divided by 6 is 1 R 3
not sure where you got the 3/2 from, i think you overcomplicated it
This is wrong and it seems you have the same misunderstanding as OP.
According to you 9^0 + 9^1 when divided by 6 has remainder 0 (because unit digit is 0), but the remainder is clearly 4.
As a rule of thumb, you never use unit digit unless you’re trying to find the remainder when dividing by 10 bc that’s what it is supposed to be.
thanks a lot man, I understood the mistake, I was simplifying the denominator which was wrong, the 10/4 , 5/2 example helped me
Sure np, but don’t forget the biggest mistake here was undoubtedly using unit digits to solve a problem unrelated to it. So, don’t forget to rectify that too.