The especially nice thing about Eulers papers is he is very keen on describing the methodology

he's a "practical" guy, that's why

remember that he was the "go-to" guy in St. Petersburg.

you need to get something computational done, you go to Euler

Is there a particular proof from that page thats worth looking at?

This caught my eye, but doesnt seem very mathematicall significant : "Letters to a German Princess on various topics in physics and philosophy"

What a player

ah... that German princess was actually interested in math. :)

:)

and had the money to get the best teacher there was ;)

what I'm saying is that it's a good one.

I'm looking at it now

An unfortunate scan.

Somebody needs to OCR this

I'm just thankful somebody took the time to scan...

quite a job to LaTeX all this stuff up but many people will be thankful if you do :p

indeed :D

Its in the campus library

Gonna go pick it up to read

brb german princess

I can see why they had trouble scanning it

its a pocket book 3" by6"

with razor thin pages

I've not read it yet

Bye

@All:Good morning everyone!

Hey Chandru ! This one is my first chat.

hi Debanjan

Man, every time I visit MO I can only understand at most two questions on their front page... :D

well you are beating me :p

:D

(well of course, not counting the CW questions, but they can get rather highbrow too)

Morning.

Could you help me with this? How do I find out what divisibility rule follows from partitioning the digits of a number into groups of two and three, respectively, starting from the right?

(This is an exercise in Erdös' "Topics in the theory of numbers".)

I need to get that book

393 is divisible by 3 because 3+9+3 is. 273459 is divisible by 30 because 27+34+59 is.

oops, it's not that simple.

hm, it says groups of 2 and 3.. you seem to by partitioning into groups of 2

unless I misunderstood the statement (which often happens).

1896246 is divisible by 33 because 1+89+62+46 is

that's better

muad, the book is available on the internet.

Weltschm what do you mean by divide in groups of 2 and 3

Statement says: "partition the digits of a number into groups of two and three, respectively, starting from the right. Treat these as two- and three- digit numbers, respectively and proceed as in the previous exercises [which are about divisibility by 9 and divisibility by 11]. What divisibility rule arises?".

yeah but what do you interpret that as meaning

(I could give you the location of the book though it'd be supporting piracy.)

Well, I thought it meant that, for instance if we have 9385450 then look at 50, 854, 93.

I thought of it as (1) turning 9385450 into [9][38][54][50] and (2) turning it into [9][385][450] to get two different divisibility tests

it would be interesting to see if you can get some results out of [ab][cde][fg][hij][kl] though

Oh, I think you're right.

So what do you think follows from (1) and (2) ?

that would be like kl + hij * 10^2 + fg * 10^5 + cde * 10^7 + ab * 10^10

there's no reason why that wouldn't give a new divisibility test for something

ah 9 and 11 are special because that's -1 and 1 mod 10

if you are in groups of two then it might 99 and 101

I'll look at that.

Actually you might get something nice out of [a][bc][d][ef][g]

hey Weltschm here is a problem: is there a power of two which has all the digits 1,2,3,4,5,6,7,8,9 in it an equal number of times?

Alright.