Maths 8 new July 2009 www

Maths 8 new July 2009 www.newland.at

Finally managed to read some interesting maths pages

My Other links maths 1 maths 2 maths 3 maths 4 math 5 math6 math7 math 8 math 9

Maths links

Jokes http://xkcd.com/482/

Fibonacci calculator http://www.plenilune.pwp.blueyonder.co.uk/fibonacci-calculator.asp

fre ib resources papers http://www.ibmaths.com/free.htm

good maths pages http://www.mathpages.com/home/index.htm

Revision guide http://www.netsoc.tcd.ie/~jgilbert/maths_site/index.html

AMS http://www.ams.org/

Biographies of woman in mathematics http://www.agnesscott.edu/lriddle/women/alpha.htm

Metric system

http://lamar.colostate.edu/~hillger/origin.html

http://lamar.colostate.edu/~hillger/dates.htm

http://lamar.colostate.edu/~hillger/internat.htm

maths writing http://ems.calumet.purdue.edu/mcss/kevinlee/mathwriting/

Number recreation http://www.shyamsundergupta.com/whatisnew.htm

360 or 365 days in a year http://www.direct.ca/trinity/360vs365.html http://www.direct.ca/trinity/orbital.html

maths papers http://front.math.ucdavis.edu/

Maths archives.uk http://archives.math.utk.edu/

Cut the knot http://www.cut-the-knot.org/collection.shtml

Baez http://math.ucr.edu/home/baez/FUN.html#mathematics

the meaning of Einsteins equation http://math.ucr.edu/home/baez/einstein/einstein.html

animated jave illustrations http://www.mathpages.com/home/polyjava.htm

German

Gierhardt .de http://www.gierhardt.de/mathematik/index.html

ramaformulas http://www.gierhardt.de/mathematik/ramaformeln.html

http://www.jahr-der-mathematik.de/ http://www.mathematikum.de/

Swiss maths http://www.mathematik.ch/

tsm resources http://www.tsm-resources.com/index.html

free electronic maths journals http://stat-www.berkeley.edu/users/mathsurv/ejournals.html

Maths is fun http://www.mathsisfun.com/numbers/addition.html

Maths in the movies http://world.std.com/~reinhold/mathmovies.html

Mathletics http://www.mathletics.com.au/

Math humour http://www.doe.virginia.gov/Div/Winchester/jhhs/math/humor/mathhumr.html

Revision guide http://www.netsoc.tcd.ie/~jgilbert/maths_site/index.html

Maths awards http://www.eff.org/awards/coop

0.999999 http://www.cut-the-knot.org/arithmetic/999999.shtml

http://mathforum.org/library/drmath/view/55746.html

http://www.jimloy.com/algebra/9999.htm

http://www.jimloy.com/math/math.htm

big numbers

http://www.isthe.com/chongo/tech/math/number/number.html

http://www.isthe.com/chongo/tech/math/number/tenpowerd.html

http://www.isthe.com/chongo/tech/math/number/tenpowerde.html

http://www.isthe.com/chongo/index.html

number theory and maths pages http://www.isthe.com/chongo/tech/math/index.html

fun wirh numbers http://www.newdream.net/~sage/old/numbers/index.html

mathseq http://www.isthe.com/chongo/mypict.html

http://www.isthe.com/chongo/photo/landon/math/eq1.png

http://www.isthe.com/chongo/photo/landon/math/eq1.png

http://www.isthe.com/chongo/photo/landon/math/eq2a.png

http://www.isthe.com/chongo/photo/landon/math/eq4a.png

continued fraction http://archives.math.utk.edu/articles/atuyl/confrac/intro.html

some more links

http://www.humboldt.edu/%7Emef2/mybookmarks.html

http://www.humboldt.edu/%7Emef2/mybookmarks.html#General%20reference-%20news,%20etc.:

http://www.humboldt.edu/%7Emef2/mathhistorysites.html

http://www.humboldt.edu/%7Emef2/mybookmarks.html#Mathematics%20Education

http://home.scarlet.be/~ping1339/index.html

http://www.lacim.uqam.ca/%7Eplouffe/inspired22.html

http://www.lacim.uqam.ca/~plouffe/

http://www.dsiegel.com/

http://www.math.harvard.edu/~elkies/Misc/index.html

http://www.math.harvard.edu/~elkies/Misc/index.html#puzzles

http://www.math.harvard.edu/~elkies/Misc/pi10.pdf

http://www.mit.edu/people/jcb/jokes/

http://www.math.harvard.edu/~elkies/chess.html

http://www.math.harvard.edu/

http://www.math.harvard.edu/~elkies/math_cv07.pdf

formulae http://www.univie.ac.at/future.media/moe/formeln/index.html

maths Olympiads china http://www.msri.org/specials/gmo

usa http://www.unl.edu/amc/e-exams/e8-usamo/usamo.shtml

http://reflections.awesomemath.org/archives.html

http://www.imo-official.org/

http://www.onlinecourses.org/2009/03/10/the-10-biggest-intellectual-fights-of-all-time/

worlds toughest maths questions

http://www.networkworld.com/community/node/33361#comment-190336

http://www.scottaaronson.com/writings/bignumbers.html

http://www.clarku.edu/%7Edjoyce/trig/

Some science, economics, maths http://www.rbduncan.com/

Animated images http://bellsouthpwp.net/e/d/edwin222/enter.htm

Maths examples http://www.meta-religion.com/Mathematics/mathematics.htm

Maths art in nature http://myweb.cwpost.liu.edu/aburns/

920^157 (mod 2668)

I found some interesting information in Applied Abstract Algebra by Rudolf Lidl (I have pasted the link above).

I liked also the challenge

Here is my reasoning, (after correcting a calculation mistake, thanks Marlene

First I write 2668 as 23x29x4.

Then it is easy to verify that

920 = 0 (mod 23) => 920^157 = 0 (mod 23)
920 = 0 (mod 4) => 920^157 = 0 (mod 4)
920 = 21 (mod 29)

The idea is then to find 920^157 modulo 29 and conclude unsing the chinese remainder theorem.

157 = 28x5 + 17 and by Fermat's little theorem, 21^28 = 1 (mod 29)
thus 920^157 = 21^157 = (21^28)^5x21^17 = 21^17 (mod 29)

To simplify 21^17 (mod 29) I don't have any really nice solution... But one can notice that 21^3 = 10 (29), thus
920^157 = 21^17 = (21^3)^5x21^2 = 10^5x21^2 (mod 29)
Because 21^2 = 6 (mod 29) then
920^157 = 10^5x21^2 = 10^5x6 = 10^4 x 60 = 10^4x2 = 20000 (mod 29)
then one is able to compute that 4000 = 27 (mod 29)

So one has to find a number x that verify the following:
x = 0 (mod 4)
x = 0 (mod 23)
x = 27 (mod 29)

Using the Chinese remainder theorem, x = 0 + 0 + 27x23x4 = 2484

What a fun problem!

I think though that Sanjeev is correct. At least, I get 4000=27(mod29), and not 19(mod 29) as Mathilde has, and following along with Mathilde's solution, gives Sanjeev's answer.

Hi all, Now it is high time that we calculated :

1) 920^1571 (mod 2668)

2) 920^15715 ( mod 2668)

3) 920^157157 ( mod 2668) Sanjeev Malhotra ,Mombai ,INDIA