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How to prove that the product of three coprime integers is divisible by $3$
I’m given the following question
Let $a$, $b$, and $c$ be coprime integers. Prove that $ab+bc+ca$ is divisible by $3$
I think it’s simple enough. Since $3$ divides $a$, it divides $ab$. Similarly $3$ divides $bc$, and $3$ divides $ca$. Since all three are divisible by $3$, the product is divisible by $3$.
How do I know that this argument works?
A:
To know your proof is correct, you only need to know a few things:
$a$, $b$, $c$, and $ab$, $bc$, $ca$ are integers.
$a$, $b$, $c$ are coprime.
Since those are all simple facts, this is straightforward.
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Citibank Limited (Chinese name: ) is the Hong Kong branch of Citicorp, one of the largest multinational banking companies in the United States. Citicorp is the forerunner of Chase Manhattan Bank, the current owner of Citibank’s branding in Hong Kong. The company was established in Hong Kong in 1930 as the Hong Kong branch of the Hong Kong and Shanghai Banking Corporation Limited (which is now Citicorp). Before the takeover by Citicorp, Hong Kong was connected to Shanghai by the Bank of China. After the takeover, Citibank Limited moved to the Bank of China building, but continued to use the name «Citicorp Hong Kong Limited». It adopted the name «Citibank Hong Kong Limited» in 2007. The company is a wholly owned subsidiary of Citicorp.
History
The history of the Bank of China began in 1866 when the Bank
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