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wu :: forums    riddles    medium (Moderators: Icarus, Eigenray, towr, ThudnBlunder, SMQ, Grimbal, william wu)    Periodic decimals coincidence? « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Periodic decimals coincidence?  (Read 374 times) JocK Uberpuzzler     Gender: Posts: 877 Periodic decimals coincidence?   « on: May 26th, 2006, 4:19pm » Quote Modify 1/11 = 0. 0 9 0 9 0 9 ...     ------>  0+9 = 9   2/11 = 0. 1 8 1 8 1 8 ...     ------>  1+8 = 9   1/7 = 0. 142 857 142 857 142 857 ...   ------>  142 + 857 = 999   2/7 = 0. 285 714 285 714 285 714 ...   ------>  285+714 = 999   1/13 = 0. 076 923 076 923 076 923 ...   ------>  076+923 = 999   2/13 = 0. 153 846 153 846 153 846 ...  ------>  153+846 = 999   3/13 = 0. 230769 230769 230769 ...   ------>  230+769 = 999   1/91 = 0. 010 989 010 989 010 989 ...   ------>  010+989=999   1/73 = 0. 0136 9863 0136 9863 ...   ------>  0136+9863 = 9999   1/17 = 0. 05882352 94117647 05882352 94117647...   ------>  05882352+94117647 = 99999999     Coincidence..?           IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. Barukh Uberpuzzler     Gender: Posts: 2276 Re: Periodic decimals coincidence?   « Reply #1 on: May 27th, 2006, 4:29am » Quote Modify No. IP Logged Eigenray wu::riddles Moderator Uberpuzzler     Gender: Posts: 1948 Re: Periodic decimals coincidence?   « Reply #2 on: May 27th, 2006, 3:50pm » Quote Modify A fraction a/n, with (10a, n)=1, has this property iff for some r>0, the order of 10 mod p has even part 2r for all primes p|n. 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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