0:00
Hello.
00:01
So here we want to show that n squared minus one is divisible by 8.
00:06
So in other words, eight divides n squared minus one whenever n is going to be an odd positive integer.
00:14
So for our basic step, when n is equal to 1, while n squared minus 1, when n is equal to 1, it's just 1 squared minus 1 is equal to 0.
00:24
And 0 is certainly divisible by 8.
00:27
0 is divisible by anything, so therefore p of 1 is true.
00:33
And then from there, we assume that p of k is true.
00:38
In other words, 8 divides k squared minus 1.
00:44
We assume that's true, and then we show that k plus, want to show that p of, well, so it's an odd integer, so therefore p of k plus 2 is going to be true, right? we only have to check odd integers here...