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wu :: forums    riddles    medium (Moderators: ThudnBlunder, Grimbal, Icarus, SMQ, william wu, towr, Eigenray)    prime « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: prime  (Read 254 times) tony123 Junior Member     Posts: 61 prime   « on: Jul 20th, 2007, 5:48am » Quote Modify find all natural numbers n whish 2^n +n^2004 is prime IP Logged jollytall Senior Riddler     Gender: Posts: 585 Re: prime   « Reply #1 on: Jul 20th, 2007, 7:21am » Quote Modify 1 to start with. All other numbers must be odd, if they exist. IP Logged Eigenray wu::riddles Moderator Uberpuzzler     Gender: Posts: 1948 Re: prime   « Reply #2 on: Jul 23rd, 2007, 3:21pm » Quote Modify And if n is odd, then 2n=2 mod 3, so unless n=0 mod 3, we will have n2004=1 mod 3 and the sum will be divisible by 3, hence not prime if n>1.  So n=3k, but 23k+n2004 = (2k+n668)(22k-2kn668+n1336 ). The first factor is > 1, and the second is at least min(2k,n668)2 > 1 also.  So the product can't be prime for n>1. 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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