Dhaka Secondary 2010/2

[BdMO]

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

[protik]

6. I am not sure about my answer..

[AntiviruShahriar]

$5^{ \phi(9)} \equiv 2^{ \phi(9)} \equiv 1$(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]

Cant we use it??
as 1024 is evan so
$5^2+2^2+1=30$ remainder 3.....

[[Actually i dont know Mod. ]]