I have most of the work done on MS221 / TMA04 but since I haven't received the results of TMA03 yet, I wait before sending the TMA in. So, I can spend my study time freely. I am currently studying ( elementary ) Number Theory. I made some real progress during the weekend and today.

I completely understand and am thus able to prove, ( now and in the future, I am sure ) the formula for the Sigma number-theoric function. The sum of the dividers of a natural number. For example:

12 = 2^2 * 3

sigma(12)

= 1 + 2 + 3 + 4 + 6 + 12

= ( 1 + 2 + 4 ) + ( 3 + 6 + 12 )

= ( 1 + 2 + 4 ) * ( 1 + 3 )

= 7 * 4

= ( 2^3 - 1 ) / ( 2 - 1 ) * ( 3^2 - 1 ) / ( 3 - 1 )

= 28.

Furthermore, I am beginning to ger a practical understanding of Möbius inversion.

And I firmly consolidated knowlegde of and skills regarding

- Properties of integer division

- Euclidean algorithm for finding the GCD

- Linear diophantine equations

- Congruences

- etc.

2-2018 Teaching by misleading

2 months ago

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