Dhaka Secondary 2010/2
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Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
What is the remainder when $2^{1024} + 5^{1024} +1$ is divided by $9$?
Re: Dhaka Secondary 2010/2
6. I am not sure about my answer..
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Re: Dhaka Secondary 2010/2
$5^{ \phi(9)} \equiv 2^{ \phi(9)} \equiv 1$(mod 9)
$5^{1020} \equiv 2^{1020} \equiv 1$(mod 9)
$5^{1024} \equiv -5 \equiv 4$(mod 9)
$2^{1024} \equiv -2 \equiv 7$(mod 9)
$7+4+1=12 \equiv 3$(mod 9)
Ans:3
$5^{1020} \equiv 2^{1020} \equiv 1$(mod 9)
$5^{1024} \equiv -5 \equiv 4$(mod 9)
$2^{1024} \equiv -2 \equiv 7$(mod 9)
$7+4+1=12 \equiv 3$(mod 9)
Ans:3
- leonardo shawon
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Re: Dhaka Secondary 2010/2
Cant we use it??
as 1024 is evan so
$5^2+2^2+1=30$ remainder 3.....
[[Actually i dont know Mod. ]]
as 1024 is evan so
$5^2+2^2+1=30$ remainder 3.....
[[Actually i dont know Mod. ]]
Ibtehaz Shawon
BRAC University.
long way to go .....
BRAC University.
long way to go .....