[Discrete Mathematics] Divisibility Examples

We do proofs with divisibility in this video.

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[arieppy]

In the last example, shouldn't it be either 8(k+1)j or 8kj (instead of 8kjk)?

[migs_dotcom]

On the Example where 8(k+1)k is divisible. How did you arrive to that? is it because k*k+1 will always equal an integer therefore it can be divided because of a=dq+r?

[thepedzed]

Where does the 8|(n²-1) come from? Is that not supposed to be 4|(n²-1)? The pinkish part at the end is a bit unclear.

[Andersl]

Could you explain a bit further why dividing with 1 causes problem?(related to the first problem)

Because the problem said A|B or A|C, now both doesnt have to be divisible so that you can get A = 6, B = 6 and C = 1. Then you will get A|BC with following A|B.

Anyways thanks a lot for making and posting these videos, have an exam in 2 days. Im a poor student but I have mentioned this channel to my math class on many occasions :)

[joshuaschwarting]

Also wondering why you replaced n with (2k+1).

[SALMalikk]

In the last example, how do we know that atleast one of them is even and the other one is odd ?

[rkcst]

I am so confused by this. What if n = 1? That means that this is saying 4 divides 0.

[jidelgado]

Oh my goodness we both used the same counterexample in problem 1

[AdityaKumar-rkrq]

then how did u show in ur first lecture that a|b, a|c then a|(b+c)....but in ur ex u r telling that 6|6 which is not valid then ur first prove was wrong.