Using your Head is Permitted

June 2009 riddle

This month's riddle was inspired in part by a suggestion from James Ge.

Let F be a finite field of order f=|F| and let c be an element in F. How many (ordered) pairs (x,y) are there that solve the equation x2+y2=c?

Answers should be closed-form functions of f and c and should be accompanied by proofs of correctness.

List of solvers:

Albert Stadler (9 June 01:43)
Dan Dima (9 June 22:34)
James Ge (12 June 20:51)

Elegant solutions can be submitted to the puzzlemaster at Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.


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