## Dhaka Secondary 2010/2

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
Forum rules
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.
BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

### Dhaka Secondary 2010/2

What is the remainder when $2^{1024} + 5^{1024} +1$ is divided by $9$?

protik
Posts: 35
Joined: Wed Dec 08, 2010 7:21 am

### Re: Dhaka Secondary 2010/2

AntiviruShahriar
Posts: 125
Joined: Mon Dec 13, 2010 12:05 pm
Location: চট্রগ্রাম,Chittagong
Contact:

### 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

leonardo shawon
Posts: 169
Joined: Sat Jan 01, 2011 4:59 pm
Location: Dhaka

### 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. ]]
Ibtehaz Shawon
BRAC University.

long way to go .....