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 January 10th, 2010, 05:31 AM #1 Newbie   Joined: Jan 2010 Posts: 1 Thanks: 0 Please help me solve this question Hi, I'm kind of new to math Olympiad and it's my first time so my teacher gave me a bunch of past questions to try but I can't seem to solve any! Can you help me with a step by step explanation please? The question is: (a) Show that the equation a^2 + b^2 = 2c^2 ......(1) has an infinite number of solutions for positive integers a,b and c; with a and b relatively prime. (b) Find all possible solutions to (1) Thanks a million!!
 January 27th, 2010, 02:28 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,927 Thanks: 2205 Hint: let a = 1 and b/c be an "odd" convergent (in lowest terms) of the continued fraction 1 + 1/(2 + 1/(2 + . . . = ?2.

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