What are some unsolved problems in math which seem easy at first glance?
Here's a good one that's slightly less well known: if and are both integers, must be an integer as well?
(This is known to be the case if you also assume that is an integer, but that's an extremely difficult theorem.)
Oh, and here's another: can you color the points of the plane in 4 colors so that no two points 1m apart have the same color? How about 5 colors? 6?
(With 3, you definitely can't (cool puzzle). With 7, you definitely can (slightly less cool puzzle). Nobody knows what the minimum number of colors is).
Here's a good one that's slightly less well known: if and are both integers, must be an integer as well?
(This is known to be the case if you also assume that is an integer, but that's an extremely difficult theorem.)
Oh, and here's another: can you color the points of the plane in 4 colors so that no two points 1m apart have the same color? How about 5 colors? 6?
(With 3, you definitely can't (cool puzzle). With 7, you definitely can (slightly less cool puzzle). Nobody knows what the minimum number of colors is).
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