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January 10th, 2010, 05:31 AM   #1
Joined: Jan 2010

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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!!
darkangel777 is offline  
January 27th, 2010, 02:28 PM   #2
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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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