Please help almost done with them

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In summary, to prove that every even perfect number is also a triangular number, we need to show that there exists an if and only if relationship between a triangle number and a square, and that this relationship also holds for perfect numbers.
  • #1
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i have two ?'s to ask yall. ok, i need to prove every even perfect number is a triangular number. the formula is t(n)= 1+2+... tn = (n(n+1))/2.

ok i know that to be a perfect number, it is sigma (a) which menas 2times a. for ex, sigma(6)=1+2+3+6=12. this is as far as i can get can anyone show me light for this?

find least residue for (n-1)! mod n for several n values and find a general rule.

alright, i know bty least residue means basically the remainder. it is in the form of a=bq + r, where r is the least residue. again, can anyone show me what I'm missing here for this problem?

please even if you are viewing this post, please say anything as to what you are thinking about the problem... :redface:
 
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  • #2
2. Look at the residues for prime n.

Then look at today's thread titled 'Prime Factorial Conjecture' in this subforum.
 
  • #3
You've asked these questions in another thread, where I've responded. In case you missed it, check [post=244396]my post[/post] along with the thread Gokul43201 suggested.
 
  • #4
For the first question, regarding triangle numbers and perfect numbers; the two facts we need to know are the form of the even perfect numbers, the only kind ever found, and a way of relating a triangle number to a perfect number. The form of the perfect number is: (2^(p-1))((2^p) -1). In this case we must have (2^p) -1 is prime and this implies that p is also prime.

Now all that is necessary is to find an if and only if relationship between a triangle number, and something like a square, and see if that also holds for a perfect number.
 
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1. What do you need help with specifically?

I am almost done with them refers to a specific task or project that I am close to completing and require assistance with.

2. How much progress have you made so far?

I have made significant progress and am close to completing the task, but there are still some final steps that I need help with.

3. What is the deadline for completing this task?

The deadline for completing this task is approaching, which is why I am seeking help to ensure that it is finished on time.

4. What type of help do you need?

I may need assistance with specific aspects of the task, such as troubleshooting an issue or completing a certain portion of the project.

5. Is there any specific knowledge or expertise required to help with this task?

Yes, since I have already made significant progress, I may need someone with knowledge or expertise in a specific area to help me complete the final steps.

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