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wu :: forums    riddles    medium (Moderators: Grimbal, ThudnBlunder, towr, Eigenray, SMQ, william wu, Icarus)    Determine all positive integers « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Determine all positive integers  (Read 328 times) tony123 Junior Member     Posts: 61 Determine all positive integers   « on: Nov 17th, 2007, 2:02am » Quote Modify Determine all positive integers a and b such that x^2 + x + 1 divides     x^a + x^b + 1 IP Logged Aryabhatta Uberpuzzler     Gender: Posts: 1321 Re: Determine all positive integers   « Reply #1 on: Nov 17th, 2007, 3:17pm » Quote Modify I get a + b = 0 (mod 3) and a =\= 0 (mod 3) by considering the complex cube roots of unity. 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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