Q. 405.0( 1 Vote )

# Prove n^{4</su }

Answer :

(as a^{2}–b^{2} = (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) n^{4} + 4 has two distinct factors and 1 as a factor.

So, n^{4} + 4 is a composite number for n > 1.

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