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# The Soc for People of 'GRDCT2008' Mk VI watch

1. Attempting to claim insomniac victory?
2. i was till you came along

but aren't i/we insane? this time..is...just....SOMETHING...t o say the least
3. Nothing better than early morning maths:
Spoiler:
Show
Theorem: For all

where is the sum of the positive divisors of , and is the number of positive integers less than n that are coprime to n.

Proof Let be the canonical decomposition of n, then

and

.

Hence

.

The upper bound follows immediately. And for the lower bound, we see that

as required.
4. ghosh

you make me cry with amazement

5. (Original post by Malsy)
you make me cry with amazement
Well, none of it was that spectacular, although it took me ages to spot the clever bit, when we decided that

6. ooo nice and simple on the right hand side of the equals sign

morning
7. Ooo:
Spoiler:
Show
Theorem: For all

where is the number of divisors of .

Proof Again, let be the canonical decomposition of . Then we find that our product can be rewritten as

where . But this is , and the result follows.

Sidenote We have an interesting abstract way to lay out all the divisors of : consider an -dimensional lattice/matrix, which is of size , and the entry at , with represents the divisor of , namely, . Then this lattice/matrix contains every divisor of once and only once.
8. Sometimes, I wish I had taken maths to A level just so I could humour Ghosh's little mathmo moments
9. (Original post by Melting Sugar.)
Sometimes, I wish I had taken maths to A level just so I could humour Ghosh's little mathmo moments
Umm, you'll find that A-level maths won't help you understand anything I've written above, not even the notation, really, however, any part you don't understand, I could probably explain to you.
10. (Original post by Melting Sugar.)
Sometimes, I wish I had taken maths to A level just so I could humour Ghosh's little mathmo moments
lol are you joking mals, Ive got less of a clue than you
all I recognise are the greek symbols and then.... its all greek to me
11. University Challenege
ftw
age difference compared to last times is obvious
lolled at the 30, 000 seconds
12. (Original post by clad in armour)
University Challenege
ftw
age difference compared to last times is obvious
lolled at the 30, 000 seconds
Same. Jeremy Paxman's face:
13. (Original post by natty_d)
Same. Jeremy Paxman's face:
yay I got the superconductor question right and she said semiconductor
14. (Original post by clad in armour)
yay I got the superconductor question right and she said semiconductor
What you upto today?
15. (Original post by natty_d)
What you upto today?
not much, read the Mail to some service users at the care home
16. (Original post by GHOSH-5)
Umm, you'll find that A-level maths won't help you understand anything I've written above, not even the notation, really, however, any part you don't understand, I could probably explain to you.
are you joking???
have you even slept?!
17. me and ghosh were up so late as you can tell by the post times

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