Let be a prime. Show that .

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- Feb 28th 2010, 10:49 AMjames_bondSum of binomials
Let be a prime. Show that .

- Feb 28th 2010, 10:49 PMNonCommAlg
it's also true for anyway, this is just a simple application of Lucas' theorem. by this theorem we have:

because every prime which is is in the form and thus

**Remark**: you might say that i didn't apply Lucas' theorem correctly for and but actually what i did

is perfectly fine because:

if then by Lucas' theorem:

similarly if then by Lucas' theorem: