Then,

First post !

I'm here just so I can ask mathematics about the proof that all D-free integer D-th roots are linearly independent. But hi! wave

Question about roots of integers

I've been wondering if the roots of the integers are linearly independent. That is, are there any equations of the form

c₁ ^D√a₁ + c₂ ^D√a₂ + ... + c_m ^D√a_m = 0

where all the c_m are rational numbers and all the a_m are D-free numbers (by analogy with squarefree)?

Eventually I found what's likely a proof of the case D = pⁿ.

So: where has this been proved before? How difficult is it? Is it, dare I hope, actually new mathematics? Is the proof correct in the first place?

(also posted to mathematics)

"Clothing Time", Largo/Erika duet

Here.

And it's drunkard found and it's drunkard lost
And we're heavy, eh, when the panicking stops
It's clothing time

(no subject)

The name "synchcola" comes from a silly thing I thought the other day.

From here, a giant buzzsaw/factory on wheels called the Bagger 288: [raise.ru]

"This is the best Tractor Fair ever!"

The second word of the headline started, "eksk", and I was like "Aha! It's one of those Russian words that have a bunch of random consonants. Wouldn't one k have been good enough? That wacky language."

It's not a Russian word; it's English, "excavator". Wheee.