Q40 of 128 Page 25

Prove n4 + 4 is a composite number for n > 1



(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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