Proof by induction of the sum of 2 squares

[aporter1]

so I've gone along with

assume: r_k=(a²+b²)
if, r_k+1=(a²+b²)(c²+d²)=(ac-bd)²)+(ad+bc)²

 

[SammyS]

so I've gone along with

assume: r_k=(a²+b²)
if, r_k+1=(a²+b²)(c²+d²)

Then r_k+1=(ac-bd)²)+(ad+bc)²

Is more like it.

 

[aporter1]

so I'm on the right track for the right side then?

 

[SammyS]

so I'm on the right track for the right side then?

What do you mean by "the right side" ?

 

[aporter1]

(ac−bd)2+(ad+bc)2

 

[Mark44]

Mod note: Moved this thread to Precalculus section.

 

[SammyS]

so I've gone along with

assume: r_k=(a²+b²)
if, r_k+1=(a²+b²)(c²+d²)=(ac-bd)²)+(ad+bc)²

Let me answer this post of yours again.

It makes sense to usea subscript with r. Did your teacher give you that idea?

You should really define r_n somewhere.

Like: Let r_n = a₁a₂a₃a₄...a_n where each a_i is the sum of two integers.

Now, let's redo what you have above with some changes that I will put in RED.

so I've gone along with

Assume: r_k=(a²+b²), for two integers, a and b.

If a_k+1 = c²+d², for two integers, c and d,

[STRIKE]if,[/STRIKE] then r_k+1=(a²+b²)(c²+d²)=(ac-bd)²)+(ad+bc)²

Therefore, r_k+1 is the sum of the squares of two integers.

 

[Mark44]

I've taken history of math discrete math

Is that two different classes or one? If it's one class, what are the prerequisites for the class you're currently in, and if there are any, did you take them and get a reasonably good grade? I get the sense that you're way over your head in this class.

, but its been a while. Its a 400 level course, its an independent study class. I've gone to my teacher for help but I don't understand

 

[aporter1]

Is that two different classes or one? If it's one class, what are the prerequisites for the class you're currently in, and if there are any, did you take them and get a reasonably good grade? I get the sense that you're way over your head in this class.

its one class, and i got good grades in the pre requisites. but see its an independent study class where its a special topics class, so my teacher just randomly picked a book

 

[SammyS]

its one class, and i got good grades in the pre requisites. but see its an independent study class where its a special topics class, so my teacher just randomly picked a book

I doubt that it was a random pick !