Q. 405.0( 1 Vote )
Prove n4 + 4 is a composite number for n > 1
Answer :
(as a2–b2 = (a + b)(a–b))
….. eq (1)
Now, n > 1
n – 1 > 0
Also, 
Therefore, 
and 
are distinct positive integers.
So, we can say that
n–1 > 0
Similarly, n + 1 > 0
Therefore, 
are also distinct.
Thus, from eq(1) n4 + 4 has two distinct factors 
and 1 as a factor.
So, n4 + 4 is a composite number for n > 1.
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