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A Fibo quadruplet (Posted on 2015-08-28) Difficulty: 2 of 5
Given four consecutive Fibonacci numbers a, b, c, and d.

Show that (ad,2bc,cd – ab) is a Pythagorean triplet.

No Solution Yet Submitted by Ady TZIDON    
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Solution solution Comment 1 of 1
c = a+b
d = b+c = a+2*b


a*(a+2*b) , 2*b*(a+b) , (a+b)*(a+2*b) - a*b

a^2 + 2*a*b , 2*b^2 + 2*a*b , a^2 + 2*b^2 + 2*a*b

Square these:

a^4 + 4*a^3*b + 4*a^2*b^2

4*a^2*b^2 + 8*a*b^3 + 4*b^4

a^4 + 4*a^3*b + 8*a^2*b^2 + 8*a*b^3 + 4*b^4

The top two add to the third. QED

Expansions of squares thanks to; they're tedious and error-prone when done by hand, especially by me.

  Posted by Charlie on 2015-08-28 11:05:46
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