Time for another problem of the week! This one doesn’t necessarily require any number-theoretic knowledge, although a little bit might help point you in the right direction. As usual, let be the set of natural numbers, i.e., the set of nonnegative integers.

Describe all functions such that for all .

Please submit solutions to **topological[dot]musings[At]gmail[dot]com** by **Sunday, November 2**, 11:59 pm (UTC); do **not** submit solutions in Comments. Everyone with a correct solution will be inducted into our Hall of Fame! We look forward to your response.

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October 27, 2008 at 12:54 am

Todd TrimbleWhen I say, “describe all functions…”, I mean of course describe with a proof that the description is correct!

October 29, 2008 at 7:14 pm

Un problemino di matematica « In teoria[...] Matematica, Teoria dei numeri | by bobcarr Il problema che vado a descrivere si trova in questo blog, un blog di matematici professionisti; questo non vuol dire che alla soluzione non ci possiamo [...]

November 4, 2008 at 5:55 am

Solution to POW-11: Preserving sums of squares « Todd and Vishal’s blog[...] in Elementary Math Problem Solving, Problem of the Week (POW) | by Todd Trimble The solutions to POW-11 are in! Or make that solution, unless you also count your hosts’: only one reader responded. [...]

November 11, 2008 at 12:43 am

Link to 43rd Carnival of Mathematics « Todd and Vishal’s blog[...] is currently hosting the 43rd Carnival of Mathematics and that the Carnival lists Todd’s POW-11 (Preserving Sums of Squares) post as one of its entries! Possibly related posts: (automatically generated)Carnival of [...]