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wu :: forums    riddles    easy (Moderators: Grimbal, SMQ, william wu, Eigenray, ThudnBlunder, towr, Icarus)    Prime triplet « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Prime triplet  (Read 436 times) NickH Senior Riddler     Gender: Posts: 341 Prime triplet   « on: Apr 15th, 2003, 2:25pm » Quote Modify Show that, if 0 < p and p2 + 2 are primes, then p3 + 2 is also prime. IP Logged Nick's Mathematical Puzzles SWF Uberpuzzler     Posts: 879 Re: Prime triplet   « Reply #1 on: Apr 16th, 2003, 7:33pm » Quote Modify This seems like sort of a trick question.  My solution (hidden): The only p with p2+2 also prime is p=3, and for that p3+2=29, prime, so the statement is true.   For all other primes, p, p2+2 is a multiple of 3. Obvious, for p=2, and the rest of the primes are either a multiple of 6 plus 1 or a multiple of 6 plus 5. Plug 6*n+1 or 6*n+5 into p2+2, and you will see it is a multiple of 3. IP Logged NickH Senior Riddler     Gender: Posts: 341 Re: Prime triplet   « Reply #2 on: Apr 16th, 2003, 8:21pm » Quote Modify Spot on!  So, in fact, p4 + 2 is also prime! IP Logged Nick's Mathematical Puzzles LZJ Junior Member     Gender: Posts: 82 Re: Prime triplet   « Reply #3 on: Apr 17th, 2003, 1:50am » Quote Modify As for proof as to why 3 is the only value of p possible, p2 (mod 3) = 1 for all odd positive integers that are not multiples of 3, so all other odd primes can be ruled out. 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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