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wu :: forums    riddles    hard (Moderators: ThudnBlunder, Eigenray, SMQ, Grimbal, william wu, towr, Icarus)    Points on a parabola « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Points on a parabola  (Read 1000 times) inexorable Full Member     Posts: 211 Points on a parabola   « on: Dec 6th, 2005, 4:12am » Quote Modify How many points can you find on the (half) parabola y=x^2, x>0, so that the distance between any pair of them is rational? This problem sounds like a geometry problem, but it is likely to require techniques in number theory. That's because, to determine if the distance between (a,b) and (s,t) is rational, you need to test whether (a-s)^2 + (b-t)^2 is the square of a rational number...and such questions typically fall into the realm of number theory. IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium => hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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