Number Theory

This hypothesis (or theory)

There are no solutions for the following equation,

np=mp1{ n }^{ p }={ m }^{ p }-1

OR

np=mp2{ n }^{ p }={ m }^{ p }-2

Where pp is a prime number,

n,mn,m are positive integers and must be bigger than 1.

Note by Luke Zhang
4 years, 8 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

Isn't this obvious, for any natural number p>2 p > 2 ?

The difference of consecutive powers is at least 2p1 2 ^ p - 1 .

Calvin Lin Staff - 4 years, 8 months ago

Log in to reply

Wait waaaaa?????????? I just gave a comment on it. Not proved it.

And u must state that mm and nn are not 0,1,10,1,-1

Julian Poon - 4 years, 8 months ago

Log in to reply

No need to state that because u already said that it must be greater than 1

Sudhir Aripirala - 4 years, 8 months ago

Log in to reply

I asked whether it is true for n^p=m^p-3 or 4 .............

Sudhir Aripirala - 4 years, 8 months ago

Log in to reply

@Sudhir Aripirala I'll give you a clue, then you can figure out for yourself:

mpnp=km^{p}-n^{p}=k

The difference between 22 consecutive powers are always more than kk.

What must kk be?

Julian Poon - 4 years, 8 months ago

Log in to reply

@Julian Poon k=k

Luke Zhang - 4 years, 8 months ago

Log in to reply

@Luke Zhang Wooaaahhhh very insightful! Illuminati!

Julian Poon - 4 years, 8 months ago

Log in to reply

@Julian Poon I understood your theorem. Very good and thanks for making me realize my mistake

Sudhir Aripirala - 4 years, 8 months ago

Log in to reply

Can this also be correct instead of 2 if we keep 3,4,5..........

Sudhir Aripirala - 4 years, 8 months ago

Log in to reply

im sorry. Im not good

Luke Zhang - 4 years, 8 months ago

Log in to reply

I was actually starting to think if this was a troll...

Julian Poon - 4 years, 8 months ago

Log in to reply

Dood, im like 10 times worse than u lol.

Luke Zhang - 4 years, 8 months ago

Log in to reply

@Luke Zhang I dun even know calculus

Luke Zhang - 4 years, 8 months ago

Log in to reply

@Luke Zhang K noted.

Julian Poon - 4 years, 8 months ago

Log in to reply

@Julian Poon Glad that u NOTED.

Luke Zhang - 4 years, 8 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...