one seems to be unable to avoid the group obtained by permuting p-adic (or q-adic) coefficients of a number. I recently discovered a congruence using these permutations and the product of two binomial coefficients that I decided to blog about. The proof is an

*indirect*consequence of Lucas and is perhaps more interesting than the result itself. One is then led to look for something related with the Carlitz polynomials, which are the function field analog of the binomial coefficients.

I put all of this into a three page pdf which, if you are interested, you can find here:

https://drive.google.com/file/d/0BwCbLZazAtweN293bkxwYUZEYVk/view?usp=sharing

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