This hypothesis (or theory)

There are no solutions for the following equation,

\({ n }^{ p }={ m }^{ p }-1\)

OR

\({ n }^{ p }={ m }^{ p }-2\)

Where \(p\) is a prime number,

\(n,m\) are positive integers and must be bigger than 1.

This hypothesis (or theory)

There are no solutions for the following equation,

\({ n }^{ p }={ m }^{ p }-1\)

OR

\({ n }^{ p }={ m }^{ p }-2\)

Where \(p\) is a prime number,

\(n,m\) are positive integers and must be bigger than 1.

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## Comments

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TopNewestIsn't this obvious, for any natural number \( p > 2 \)?

The difference of consecutive powers is at least \( 2 ^ p - 1 \). – Calvin Lin Staff · 2 years, 5 months ago

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im sorry. Im not good – Luke Zhang · 2 years, 5 months ago

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– Julian Poon · 2 years, 5 months ago

I was actually starting to think if this was a troll...Log in to reply

– Luke Zhang · 2 years, 5 months ago

Dood, im like 10 times worse than u lol.Log in to reply

– Luke Zhang · 2 years, 5 months ago

I dun even know calculusLog in to reply

– Julian Poon · 2 years, 5 months ago

K noted.Log in to reply

– Luke Zhang · 2 years, 5 months ago

Glad that u NOTED.Log in to reply

Can this also be correct instead of 2 if we keep 3,4,5.......... – Sudhir Aripirala · 2 years, 5 months ago

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

And u must state that \(m\) and \(n\) are not \(0,1,-1\) – Julian Poon · 2 years, 5 months ago

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– Sudhir Aripirala · 2 years, 5 months ago

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

– Sudhir Aripirala · 2 years, 5 months ago

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

\(m^{p}-n^{p}=k\)

The difference between \(2\) consecutive powers are always more than \(k\).

What must \(k\) be? – Julian Poon · 2 years, 5 months ago

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– Sudhir Aripirala · 2 years, 5 months ago

I understood your theorem. Very good and thanks for making me realize my mistakeLog in to reply

– Luke Zhang · 2 years, 5 months ago

k=kLog in to reply

– Julian Poon · 2 years, 5 months ago

Wooaaahhhh very insightful! Illuminati!Log in to reply