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MaBloWriMo 23: contradiction!

So, where are we? We assumed that is divisible by , but is not prime. We picked a divisor of and used it to define a group , and… 320 more words

Number Theory

MaBloWriMo 22: the order of omega, part II

Yesterday, from the assumption that is divisible by , we deduced the equations


which hold in the group . So what do these tell us about the order of ? 196 more words

Number Theory

So we think we're a user-centred, agile team...

Yeah, we’re user-centred!

  1. Who are the people most present when our service is delivered?
  2. Where are they, physically and emotionally, at that moment?
  3. What could each of them put into our service, and what could they get out of it?
  4. 118 more words

MaBloWriMo 21: the order of omega, part I

Now we’re going to figure out the order of in the group .

Remember that we started by assuming that passed the Lucas-Lehmer test, that is, that is divisible by . 300 more words

Number Theory

MaBloWriMo 20: the group X star

So, where are we? Recall that we are assuming (in order to get a contradiction) that is not prime, and we picked a smallish divisor (“smallish” meaning ). 134 more words

Number Theory

MaBloWriMo 19: groups from monoids

So, you have a monoid, that is, a set with an associative binary operation that has an identity element. But not all elements have inverses, so it is not a group. 288 more words

Number Theory

MaBloWriMo 18: X is not a group

Yesterday we defined

along with a binary operation which works by multiplying and reducing coefficients . So, is this a group? Well, let’s check:

  • It’s a bit tedious to prove formally, but the binary operation is in fact associative.
  • 185 more words
Number Theory