Give a reason for your answer. Assume that all variables represent integers.
If n = 4k + 1, does 8 divide n2 − 1?
We have to give a reason for our answer. Let all variables represent integers. We have to If n = 4k + 1, does 8 divide n2 − 1?
8 divide − 1 :-yes
Using definition of divisibility, if m and e are integers, then m is divisible by e only if m=ec, for some integer c.
Suppose that n=4k+1
Put value of n in − 1 we get
From the definition of divisibility
And is an integer because k is an integer and sums and product of integers are integers.
Therefore, − 1 is divisible by 8.