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


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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