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wu :: forums    riddles    easy (Moderators: Grimbal, Icarus, towr, william wu, Eigenray, SMQ, ThudnBlunder)    Sum of two squares equals a cube « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Sum of two squares equals a cube  (Read 772 times) NickH Senior Riddler     Gender: Posts: 341 Sum of two squares equals a cube   « on: Feb 28th, 2004, 4:44pm » Quote Modify How many integer solutions are there to a2 + b2 = c3? IP Logged Nick's Mathematical Puzzles Eigenray wu::riddles Moderator Uberpuzzler     Gender: Posts: 1948 Re: Sum of two squares equals a cube   « Reply #1 on: Feb 28th, 2004, 8:15pm » Quote Modify There are :: infinitely many :: Probably the easiest way to see this is to consider :: powers of 2 :: But in general, :: c3 is the sum of two squares iff every prime q that divides c and is 3 mod 4 appears with even exponent in c :: « Last Edit: Feb 28th, 2004, 8:15pm by Eigenray » 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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