Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: perfect square

Hi addi;

We will get to the solution of this in a second first let me talk a little bit about what you wrote.

I am a student working on my BA degree in Mathematical Sciences. Up until about a year ago I thought I was pretty good in math because I usually got an A grade in my classes.

However, I am realizing that I am probably the least knowlegable and least experienced Mathematician out there. So I have joined this forum and others to get help and practice and hopefully experience.

I was just reading this from an American student.

I hate and fear mathematics. All they make us do is study proofs by guys who are so smart and whose methods are so bizarre and unconventional that no one other than them would think of them. Typically there are 6 - 8 of these on every exam and I just memorize the proofs and write em down. This makes my professor very happy.

This is the state of American mathematics. Thanks to our school system everyone thinks math is a spectator sport. You just read what Lagrange and Legendre and Poincare and Gauss did and memorize it. I have never seen any such person who knew every theorem as ever being good at math. The real meat of mathematics is in problem solving. You joining forums is a step in the right direction.

That is why I gave you those 2 equations. They are worthless for a solution although they do give a nice hint for the programming. I wanted you to work on the problem a little bit.

When I posted post#3 I already had a
full solution. Since juan never came back to this thread, I never posted it. If you need to see it we can look at it together.

See you in a little bit, have to do a chore.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

addi

Member

Registered: 2012-05-23

Posts: 8

Re: perfect square

Okay I know that both equations are equal so we can probably just worry about solving for one of them.

Now:

n is just a constant? Correct? So,

???

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: perfect square

Hi addi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: perfect square

Wow,awsome! Of course,you did forget that x and y values can be interchanged. But,good work!

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: perfect square

Nope!? I did not forget that.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

addi

Member

Registered: 2012-05-23

Posts: 8

Re: perfect square

why are we using

Is that the definition of a perfect square? Could we have used

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: perfect square

So that we can bound the x^2 + 3y between two squares that differ by two. For instance between 4^2 and 6^2. That way if x^2 + 3y is a square it has to equal (x+1)^2.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

addi

Member

Registered: 2012-05-23

Posts: 8

Re: perfect square

Okay here is what my brain is telling me. I can't quite figure out what you did but tell me if my thought process is wrong.

and

are the two equations, we want to know what x and y values in each equation give us perfect square answers. To do that we have to make both equal to a perfect square. Like you said earlier n^2 and m^2, but n^2 and m^2 are just constants. This means we can use any number but we cannot say that one or both of the equations are equal to a certain number per se, so we have to make them equal to an expression? Like (x)^2, but we already have an x^2 so we need to find a better expression like

correct? So now we can say

If I am on the right track then I will go back and finish looking at your solution to see if I can figure the rest out, if I am not then please correct me.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: perfect square

Hi;

When you agree that this line is true then it becomes easier. Notice the supposed square x^2+3y is bounded by 2 squares that differ by 2, like 8^2 and 10^2.

If x^2+3y is a square then it must be 9^2. That changes the above inequalities to an equation,

Now we can solve for x and y.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.