BdMO Online Forum

what is the remainder when $2^{1024} +5^{1024} +1$ is divided by $9$?
the answer given in KMC website is 0 . but i am having the same answer $3$
$2^3\equiv -1\bmod{9}$ $\Rightarrow 2^{1024}\equiv -2\bmod{9}$
$5^6\equiv 1\bmod{9}$ $\Rightarrow 5^{1024}\equiv 4\bmod{9}$
so $-2+4+1=3$ , where is the faulty?

my ans is also 3!!!!!!!!!

Yeah! I had also got it $3$. I think it would be $mod 3$ instead of $mod 9$.
Btw who understood that $S_n(x)$

i am not understanding .... . Going to PM moon bhaya

at first, $2^{6n+4}\equiv1 (mod 3)$
again, $5^{6n+4}\equiv1 (mod 3)$
so $2^{1024}+5^{1024}+1\equiv1+1+1=3 (mod 3)$

The question in Dhaka was:
What is the remainder when $2^{1024} + 5^{1024}$ is divided by $3$?
The answer is $2$

Avik Roy wrote:The question in Dhaka was:
What is the remainder when $2^{1024} + 5^{1024}$ is divided by $3$?
The answer is $2$

that was for the H.secondary .
the problem i gave was from the secondary group .

sorry, I just noticed that this was a question in the secondary category....
The answer is $3$, if all of us are not mistaken.
However, there were a few corrections when the scripts were checked. So if the official solution was initially misprinted, it was corrected later.

oh thanks for the clarification . i was stumped to the answer .

Ascha tushar tumi j rule a rule a math ta korle ata congruence na onno kishu .amake janao.pls