Hello, shosho!
Here are the factoring problems .. .
1a) Factor: .
Therefore: .
You won't like this one . . . I promise!1b) .
We have: .
Therefore: .
. . . . . .
. . . . . . . . . . Wow!
Hello again, shosho!
The second problem requires some divisibility theorems.
For a positive integer :
. . is always divisible by
. . is divisible by for odd
2) Prove that: . is divisible by 174.
Hence, is divisible by 2.
From [1]: is divisible by
. . . .and is divisible by
Hence, is divislble by 3.
We have: .
. . From[2], this is divisible by:
. . From [2], this is divisible by
Hence, is divisible by 29.
Since is divisible by 2, 3 and 29, is divisible by: