Let a = 43^8765 - 34^5678,
and let c = 43^8765 + 34^5678.
Without evaluating:
1. Show that a is divisible by 3
2.Find the remainder when c is divided by 7
3. Hence find the remainder when c^a is divided by 7.
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*
.