ankeet's blog

Can anyone prove this?
By ankeet, history, 10 years ago, In English

I'm having a little trouble proving the following:

If

then

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Here's what I came up with:

. And we can write k as c·m + d, with d < m.

So we want to show that .

The left hand side obviously simplifies to d.

On the right hand side we get: . The c·m·b vanishes, because of the modulo. And since d < m, d·b mod (m·b) = d·b. So it simplifies to too, which completes the proof.

Hope that helps :)

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