1. ## Obedient figures/numbers

Lisa calls a natural number obedient if she can be written as a product of the two figures following on each other. Example: The number 20 is obedient, because 20 = 4∙5.
Points: To every obedient number there is at least one second obedient number which proves an obedient number with the first one multiplied again.
Example: 2∙3=6 and 3∙4=12 and 6∙12=72 which is: 8∙9
Is the sentence true??Why?? Is there a proof?

2. ## Obedient numbers

Lara calls a natural number obedient if she can be written as a product of the two figures following on each other. Example: The number 20 is obedient, because 20 = 4∙5. Points: To every obedient number there is at least one second obedient number which proves an obedient number with the first ones multiplied again. 2 times 3 is 6 // 3 times 4 is twelve // 6 times twelve is 72 and 72 is 8 times 9 // Is there an Abstract proof for this sentence?

3. I'm not at all sure I understand the question.

As I understand it, an "obedient number" is one that is the product of two consecutive integers, n(n+1) for some integer n.

But how is the second number supposed to be related to the first? What does "with the first one multiplied again" mean?

Possibly you mean that if m = n(n+1) is an obedient number, then m times something else will be an obedient number as well; but that is obviously true, since m(m+1) will be obedient. Your example looks like you must mean something more than that.

4. "two figures following each other"

First, this is impossible without a closed path (maybe a circle) -- Better definition, please.

Second, (Dog Stick Figure) => (Cat Stick Figure) -- (running in a circle)

Demonstrate this multiplication.

Seriously improved definition and problem statement, please.

5. ## Obedient numbers

Originally Posted by Dr.Peterson
I'm not at all sure I understand the question.

As I understand it, an "obedient number" is one that is the product of two consecutive integers, n(n+1) for some integer n.

But how is the second number supposed to be related to the first? What does "with the first one multiplied again" mean?

Possibly you mean that if m = n(n+1) is an obedient number, then m times something else will be an obedient number as well; but that is obviously true, since m(m+1) will be obedient. Your example looks like you must mean something more than that.
Hello Dr. Peterson!
Thank you for your answer! The exercise wants me to prove the following:
Each obedient number m=n(n+1) can be multiplied with at least one other obedient number like o=p(p+1) or in different words for each m exists at least one other obedient number like for example o which than, multiplied with the first obedient number, will produce a third obedient number. So m times o is y and y=x(x+1)
How the second obedient number is related to the first one is not really defined, only with: there is at least one second obedient number which will - multiplied with the first obedient number - produce a third obedient number.
I just found an example that matches with 2 times 3 is 6 and 3 times 4 is 12 Those two obedient numbers: 6 times 12 produce 72 which is a third obedient number whereas 8 times 9 is 72.
I hope this shows the Problem in a better way!?
Sincerly, Yours Enoimreh

6. ## dog and cat

Originally Posted by tkhunny
"two figures following each other"

First, this is impossible without a closed path (maybe a circle) -- Better definition, please.

Second, (Dog Stick Figure) => (Cat Stick Figure) -- (running in a circle)

Demonstrate this multiplication.

Seriously improved definition and problem statement, please.
They both know karate, will stop to run and decide that they do not need a circle, because of their respect for each other.

7. Nice try, but they are still different species and multiplication is unlikely.

So, m(m+1) * n(n+1) = q(q+1)

Well, there are only 13 choices for q. Check them all out. Can the LHS be so factored?

8. Originally Posted by tkhunny
Nice try, but they are still different species and multiplication is unlikely.

So, m(m+1) * n(n+1) = q(q+1)

Well, there are only 13 choices for q. Check them all out. Can the LHS be so factored?
Thank you for trying. I followed your idea till I found the twenteeth possibility.

m(m+1) * n(n+1) = x = q(q+1)

01*02=02 02*03=06 12=03*04
02*03=06 03*04=12 72=08*09
03*04=12 04*05=20 240=15*16
20xxxxxxx 05*06=30 600=24*25
30xxxxxxx 06*07=42 1260=35*36
42xxxxxxx 07*08=56 2352=48*49
56xxxxxxx 08*09=72 4032=63*64
72xxxxxxx 09*10=90 6480=80*81
90xxxxxxx 10*11=110 9900=99*100
110 * 132= 14520=120*121
132 * 156= 20592=143*144
156 * 182= 28392=168*169
182 * 210= 38220=195*196
210 * 240= 50400=224*225
240 * 272= 65280=255*256
272 * 306= 83232=288*289
306 * 342=104652=323*324
342 * 380=129960=360*361
380 * 420=159600=399*400
420 * 462=194040=440*441

What I can see is, that if
m(m+1) * n(n+1) = x = q(q+1)
than
m(m+1) is related to q because q is:
first m(m+1) plus 1
second m(m+1) plus 2
third m(m+1) plus 3
and so forth.
twenteeth possibility I showed q is m(m+1) plus 20

I think that continues ..... and is infinite
but how do I put this in a proof????????

And also this is only one way to find the second obedient number, it could also be found in a different way like I don't know how, but I have to exclude it in a proof.

Thank you very much, Sincerly, E.

And what does LHS mean?

9. Originally Posted by enoimreh7
And what does LHS mean?
LHS = Left Hand Side

Not a proof. One must show them ALL.

10. Originally Posted by tkhunny
LHS = Left Hand Side

Not a proof. One must show them ALL.
First an equation, than use the equation. Do you really mean there is no equation? Sincerly, E.

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