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Category:Creative Technology Limited products
Category:Audio equipment manufacturers of the United KingdomQ:
Question about the Fermat-Weil theorem
If Fermat’s last theorem is valid, then it is true that if $p$ is prime and $a$ is coprime to $p$, then $a^{p-1} + a^{p-2} + \cdots + 1 \equiv 0 \bmod p$ or $a^{p-1} \equiv 0 \bmod p$, right?
Therefore, it seems to me that the following statement would be true, by applying Fermat’s last theorem:
$a^{p-1} + a^{p-2} + \cdots + 1 \equiv 0 \bmod p$ or $a^{p-1} \equiv 0 \bmod p$ implies that $a^{p-1} + a^{p-2} + \cdots + 1 \equiv 0 \bmod p$.
However, I tried to prove the given assertion, but the following argument does not prove the statement.
$\begin{align}
a^{p-1} + a^{p-2} + \cdots + 1 &\equiv 0 \bmod p \\
a^{p-1} &\equiv 0 \bmod p \\
a &\equiv 0 \bmod p \\
\text{false} &\text{since $a
ot\equiv 0 \bmod p$}
\end{align}$
I wonder what is wrong with my argument.
A:
When you write
$$a^{p-1} + a^{p-2} + \cdots + 1 \equiv 0 \bmod p$$
note that the sum doesn’t mean $0$ mod $p$. It means $a^{p-1} + a^{p-2} + \cdots + 1 \in \mathbb{Z} / p\mathbb{Z}$. This is the same as saying that $a^{p-1} \equiv 0 \bmod p$, and only that. And when you do that, you get
$$\underbrace{a^{p-1} + a^{p-2} + \cdots + a}_{\text{by https://blogup.in/upload/files/2022/06/HsTs5rL5IgbHdlAGIFiy_07_2e241ac273847c4b5804c425556dccd8_file.pdf
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Category:Audio hardwareOTTAWA – Marco Rubio is from Miami, and that means he’ll do anything to honor his hometown pride.
In an interview with Maclean’s on Monday afternoon, the senator from Florida was asked how he tries to raise funds for his presidential bid. In a very emphatic way, he immediately responded: “I sell T-shirts.”
Rubio was in Toronto with his wife,
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, for the start of a weeklong tour through Canada that’s designed to highlight the Sunshine State’s advantages compared to his native Puerto Rico. He’s touring — in some cases for the very first time — various cities in the Great White North, where he said the reception he’s gotten has been “overwhelming.”
As part of his pitch to Canadians, Rubio is doing a campaign stop in Montreal this afternoon at a local baseball stadium where people can pay a $20 fee to meet the senator and pose for photos with him and his wife.
It’s all part of an effort to try and ensure the Cuban-American politician can build on his strong debate performance in the U.S. Republican primary earlier this month. That debate came right after Rubio’s one-time rival, retired neurosurgeon
Ben Carson
, left the race after admitting he struggled to make the Republican contest competitive against Donald Trump.
“As the only one of the three remaining candidates from the Republican side who’s won a state before, I think I have a leg up on the other two with how to relate to voters,” Rubio told Maclean’s.
Rubio, who has been endorsed by Canadian business mogul
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“Joe Biden was vice president of the United States, and he has a very unique story to tell. Hillary Clinton was secretary of state. That’s interesting. One was vice president of the United States and the other was secretary of state. And I think I’m most suited to tell a story of what’s happening to the American family.
“Whether people like it or not, as more and more immigrants come to this country, it doesn’t require any actual skill to come here to be successful. But in order to deal
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