1) and , so
.
2) and , so
.
3)
, so the sequence is 2,4,1,2,4,1,2,4,1,... . Since a is divisible by 3, the remainder must be 1.
Hello, nacknack!
Are you allowed Modulo Arithmetic?
Let
Without evaluating:
1. Show that is divisible by 3.
We have: .
Hence: .
. - . . . . .
Therefore: . . . . . is divisible by 3.
2. Find the remainder when is divided by 7.
We have: .
Hence: .
. . . . . . .
When is divided by 7, the remainder is 2.
3. Hence find the remainder when is divided by 7.
We already have: .
Hence: .
. . . . . . . .
We have: .
. . . . . . . . . .
When is divided by 7, the remainder is 1.
But check my work . . . please!
edit: Black was too fast for me (and briefer, too!) . . . *sigh*
.