#Mathematical profethy

1 messages · Page 1 of 1 (latest)

fickle raft
#

A misterious mathematician has revealed that there is a way to solve the following equation without using any type of calculator. He cannot show how tho, arguably because the process is too large to fit in the margins of a discord message.

I am looking for a powerful mathematician willing to take on this challenge and become the greatest of all people on this server.

drowsy agateBOT
#
  1. Wait patiently for a helper to come along.
  2. Once someone helps you, say thank you and close the thread with:
+close
  1. Feel free to nominate the person for helper of the week in #helper-nominations
fickle raft
#

$\log_x(x! + x) = 3$

shut fjordBOT
#

Miguel

650257000755888146.png
polar trench
#

HAHAHHAA

olive silo
#

lol

fickle raft
#

The mysterious mathematician is called @potent apex, by the way

polar trench
#

x^3=x!+x

#

x^3=x((x-1)!+1)

fickle raft
polar trench
#

x^2=(x-1)!+1 and now just bash it

#

easy

fickle raft
#

x(x+1)(x-1) = x!

fickle raft
#

I don't see how would you do that without a calculator

potent apex
#

Actually, I got it down to (x - 2)! = x + 1.

polar trench
#

all factorials:
1 2 6 24 120 720

#

now add 1 and see if any like

#

are a perfect square

#

24 and 120 work

potent apex
polar trench
#

OOPS

#

not all

#

LMAO

#

and then 24=4! so x=5

#

perfectly, 5^2=24+1

#

yay :D

#

120 is 5! so x is 6 and well

#

and it’s pretty clear from here that it wouldn’t work for any value of x

potent apex
polar trench
#

yes

#

from this example we can see that any future value of x will not equal to (x-1)!+1

#

I suck at proofs but it’s like

potent apex
#

Because (x - 2)! grows geometrically, while x + 1 grows only arithmetically.

polar trench
#

yes

#

thank you !!

potent apex
#

Remember your series comparisons: n! > n^k for sufficiently large n.

fickle raft
potent apex
# fickle raft How? 
x! + x = x^3
(x - 1)! + 1 = x^2
(x - 1)! = x^2 - 1 = (x - 1) * (x + 1)
(x - 2)! = x + 1```
fickle raft
#

Nice

#

You still need a calculator at that point tho

polar trench
quiet elk
muted lion
#

Exactly

fickle raft