Writing an integer as the sum of powers of phi

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SUMMARY

The discussion centers around an online applet that converts integers into sums of powers of phi, specifically exponents that sum to a given integer. An example provided is the integer 521, which corresponds to the exponents -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12. The original applet's location is unknown, and users are encouraged to share any information about it. Additionally, a method for performing this calculation by hand is referenced through a website that explains the process.

PREREQUISITES
  • Understanding of the golden ratio (phi)
  • Basic knowledge of exponentiation
  • Familiarity with integer properties
  • Ability to navigate mathematical resources online
NEXT STEPS
  • Research the properties of the golden ratio (phi) and its applications in mathematics
  • Explore integer representation techniques in number theory
  • Learn how to manually calculate sums of powers of phi
  • Investigate online mathematical tools and applets for integer analysis
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Mathematicians, educators, students studying number theory, and anyone interested in the properties of the golden ratio and integer representations.

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A while back, I found an online applet that was located on the front page of the mathematics department website for some American university. The problem is that I can't remember which university it was, and I'm not succeeding in several searches.

Basically, the way it worked was, you type in any integer, and it produces the exponents of phi that sum to your number. For example, if the number was 521, the exponents would be -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12 (which is a nice little pattern...)

Anyway - does anyone know what I'm talking about? Do you know the website I'm referring to? It's quite possible that it has been taken down...

Failing this, is there any method you know of doing this by hand?

Thanks!
 
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Thanks! I had disregarded this site since I found it so hard to read. But, upon finding no other sites, I tried again, and it actually makes a lot of sense.
 

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