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wu :: forums    riddles    medium (Moderators: Icarus, towr, SMQ, Eigenray, william wu, ThudnBlunder, Grimbal)    Counting Squares « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Counting Squares  (Read 406 times) Michael Dagg Senior Riddler     Gender: Posts: 500 Counting Squares   « on: Apr 25th, 2009, 8:59am » Quote Modify For  n>=1 ,   how many squares are in the sequence   18, 69, 154, ... , 17n^2 + 1  ? « Last Edit: Apr 25th, 2009, 9:03am by Michael Dagg » IP Logged Regards, Michael Dagg towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Counting Squares   « Reply #1 on: Apr 25th, 2009, 2:14pm » Quote Modify Aren't there infinitely many if there is at least one?   It's a Pell equation one solution to k2 - 17n2 = 1 is k1=33, n1=8   more solutions i=2..inf: ki =  ki-1 k1 + 17 ni-1 n1   ni =  ki-1 n1 + ni-1 k1     [edit]Oh wait, you probably mean up to a given n. There should be solutions regularly spaced among the convergents of the continued fraction of sqrt(17)[/edit] « Last Edit: Apr 25th, 2009, 2:18pm by towr » IP Logged Wikipedia, Google, Mathworld, Integer sequence DB 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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