hey im having some trouble with these two problems ..any help would be great
Factor:
1a) x^8 + 2x^4y^4 + 9y^8
b) a^4 +b^4 + c^2 - 2(a^2b^2 + a^2c + b^2c)
2) prove that
20^22 - 17^22 +4^33 -1
is divisible by 174
thanx in advance
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: