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wu :: forums    riddles    medium (Moderators: Icarus, SMQ, towr, Eigenray, Grimbal, william wu, ThudnBlunder)    A Prime Number And Power Puzzle « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: A Prime Number And Power Puzzle  (Read 266 times) K Sengupta Senior Riddler     Gender: Posts: 371 A Prime Number And Power Puzzle   « on: Jul 13th, 2007, 9:48am » Quote Modify A is a prime number while B and C are positive integers with B  not equal to 11 and C>=2.   Analytically determine all possible solutions to this equation:   2A + 3A= 11*BC « Last Edit: Jul 13th, 2007, 10:04am by K Sengupta » IP Logged SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: A Prime Number And Power Puzzle   « Reply #1 on: Jul 13th, 2007, 10:15am » Quote Modify 2A + 3A = 0 (mod 11) implies A = 5(2N+1) for some integer N, therefore A prime implies A = 5.   Thus 25 + 35 = 275 = 11*25 implies BC = 25.  Therefore B = 5 and C = 2.   --SMQ IP Logged --SMQ Archae Junior Member     Posts: 111 Re: A Prime Number And Power Puzzle   « Reply #2 on: Jul 13th, 2007, 1:21pm » Quote Modify How do you know that 2^A + 3^A = 0 (mod 11) implies that A = 5(2N+1)?  Am I being oblivious and missing something?  Thanks in advance for the explanation. IP Logged SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: A Prime Number And Power Puzzle   « Reply #3 on: Jul 13th, 2007, 1:43pm » Quote Modify A | 2A (mod 11) | 3A (mod 11) | 2A+3A (mod 11) ---- + ------------ + ------------ + ---------------- 0 | 1 | 1 | 2 1 | 2 | 3 | 5 2 | 4 | 9 | 2 3 | 8 | 5 | 2 4 | 5 | 4 | 9 5 | 10 | 1 | 0 6 | 9 | 3 | 1 7 | 7 | 9 | 5 8 | 3 | 5 | 8 9 | 6 | 4 | 10 10 | 1 | 1 | 2   So the pattern repeats every 10, and the only A's with a sum of 0 (mod 11) are A = 5 (mod 10).   --SMQ IP Logged --SMQ Archae Junior Member     Posts: 111 Re: A Prime Number And Power Puzzle   « Reply #4 on: Jul 15th, 2007, 10:13pm » Quote Modify Thanks, SMQ.  I wasn't as rigorous as I should have been before asking the question.   Now I know. 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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