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Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

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2024/03/01 13:26
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Liubo (ancient Chinese board game)plugin-autotooltip__plain plugin-autotooltip_bigLiubo (ancient Chinese board game)

Liubo 六博 is an ancient Chinese board game for two players.

Historians have determined that it was invented no later than the middle of the 1st millennium BCE - being popular during the Han dynasty (202 BCE – 220 CE).
The Littlewood conjectureplugin-autotooltip__plain plugin-autotooltip_bigThe Littlewood conjecture

The Littlewood Conjecture, proposed by UK mathematician John Littewood in 1930, states that for any two real numbers α and β,

$${\displaystyle \liminf _{n\to \infty }\ n\,\Vert n\alpha \Vert \,\Vert n\beta \Vert =0,}$$

where $${\displaystyle \Vert x\Vert :=\min(|x-\lfloor x\rfloor |,|x-\lceil x\rceil |)}$$ is the distance to the nearest integer.

In plain language :

Any two real numbers α and β can be simultaneously approximated at least moderately well by rationals…
The Newman conjectureplugin-autotooltip__plain plugin-autotooltip_bigThe Newman conjecture

The Newman conjecture was created by Morris Newman in 1960. It remains unsolved.

It's stated formally as :

For any integers m and r such that $${\displaystyle 0\leq r\leq m-1}$$ $${\displaystyle 0\leq r\leq m-1}$$the value of the partition function $${\displaystyle p(n)}$$ satisfies the congruence $${\displaystyle p(n)\equiv r{\pmod {m}}}$$ for infinitely many non-negative integers
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