CJ Cui @ccui

@shawnduffy @shawnduffy - let the tradition continue. This years Home Alone trivia: what’s the name of the movie Kevin was watching (on video tape)? I just noticed it tonight

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CJ Cui @ccui

6 years ago

@shawnduffy Very nice @shawnduffy! I just noticed it this morning. Every year I learn something new!

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CJ Cui @ccui

4 years ago

@ElsecallerLiz Some options are better than others 😀

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CJ Cui @ccui

4 years ago

@Bob64St @pickover e to the power of ln2

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In the U.S., businesses are on alert after the Department of Homeland Security warned of Russian cyber attacks on infrastructure and banking systems. A former FBI cyber division deputy assistant joins us to discuss how American businesses can protect themselves.

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Cliff Pickover @pickover

4 years ago

This is a mathematics joke. Retweet if you "get" it.

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CJ Cui @ccui

5 years ago

@shawnduffy Log4j

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CJ Cui @ccui

5 years ago

Apple, MSU open Developer Academy in Detroit. Partnership creates new opportunities for careers in the iOS app economy

MSU @michiganstateu

5 years ago

MSU and Apple opened its Developer Academy in Detroit, the first in the U.S.

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CJ Cui @ccui

5 years ago

@ObviousSay @pickover Found another quote from Neumann -““If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”

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CJ Cui @ccui

5 years ago

@ObviousSay @pickover John von Neumann once said something like “if you only prove something using induction, you don’t really understand the problem.” I tried to search for this quote but couldn’t find it.

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CJ Cui @ccui

5 years ago

@pickover This is the expansion of right side. The shaded terms add up to n^3. One can easily use 1, 2, 3 as examples. For general n, we can just use the simple formula 1+2+…+(n-1)=n(n-1)/2, which is something Gauss easily figured out in elementary school

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CJ Cui @ccui

5 years ago

@pickover It is true. We can use this picture to explain/prove

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CJ Cui @ccui

5 years ago

@pickover (2/2) Then among p-1, p, p+1, p+2 there is one and only one multiple of 4. It cannot be p or p+2 since both are odd, so either p-1 or p+1 is a multiple of 4. The other one is also even, so (p-1)(p+1) is a multiple of 8.

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CJ Cui @ccui

5 years ago

@pickover (1/2) Actually p^2 - 1 =(p-1)(p+1) must be a multiple of 24, based on a simple fact that any among n consecutive integers there is exactly one integer divisible by n. So among p-1, p, p+1 there is one multiple of 3. It cannot be p, so either p-1 or p+1 is a multiple of 3.