In 1967, Lander and Parkin found a fifth power equal to FOUR fifth powers : 144⁵=133⁵+110⁵+84⁵+27⁵
They also found a sixth power equal to SEVEN sixth powers: 1141⁶=1077⁶+894⁶+702⁶+474⁶+402⁶+234⁶+74⁶

We are trying to find a sixth power that is equal to SIX sixth powers.

When we will find a sixth power that is equal to six sixth powers, we will start searching a sixth power that is equal to five sixth powers !

2) How can I install Euler2000 ?

First, download the zip file, extract it into a specific directory.

At the first run, Euler2000 will detect your processor and will install itself.
Then the program will run in the background taking all idle processor time.
This means that your applications won't slow due to its use, except if you have not enough memory.

3) How can I join EulerNet ?

Go to the menu Test/User Information.
Enter your name/email/team name/password (everything is optional here).

Then click on the type of connection you have.
If you have a modem, click on Dial-up connection, and if you have a permanent access, choose Network connection.
Then click OK.

Now, go to the menu Test/Enter EulerNet, and choose the type of work (currently, only 6th power is available).
Enter the amount of work you'd like. If you have a permanent access, let the default value.
If you have a dialup connection, and you are connected every day, I recommend you the value 16.
If you are connected less regularly, you'll better reserve 64 ranges or more.
BEWARE ! There is a small bug in version 4.21b, which allows you to assign more than 100 ranges !
The server CANNOT assign more than 100 workunits to every user.

The server is euler.myip.org port 21. It is hosted by Greg Childers.

4) How can I join or create a team ?

Setting up a team is really easy. When you enter your user information, simply enter your Team Name, and all your computation time will be credited to this team (and also to you, as an individual). If you change the Team Name, all your credits change of team too ! Password is used only to avoid credit stealing, so you don't need to give it to your team.

5) What is the minimal configuration for running Euler2000 ?

It runs pretty well on any Pentium-like, but I strongly recommend that you have more than 32 megabytes (currently, Euler2000 needs 16 megabytes to compute (6,1,6) but when we will reach 2,000,000, it will surely need 24 megabytes or more).
It's pretty slow on Athlon.

6) How can I force a connection to EulerNet ?

In the menu Test, click on Enter EulerNet, then click OK. All your work will be sent back to the server if you are connected to the Internet.
All your assigned work remains assigned to your computer for a period of 30 days. That means that when no result has been received after 30 days, the values are reassigned to another participant.

7) I'm getting Timeout errors, is this normal ?

Yes, in fact, the current behaviour of the server is that every connected participant has 60 seconds to send back all his work and to get his future tasks and check if the work-in-progress is correct. Since it's common that you need more than 64 ranges, it takes a lot of time to get all this work, so you'll get disconnected.
This behaviour of EulerNet will change very soon.

8) I get a 'proxy server does not support tunneling' and 'proxy authorization required', what does that mean ?

Well, in fact, it is a bug in Euler2000. For the moment, Euler2000 is unable to bypass proxies. Next version will solve the problem, but also, working on every new version is very time-consuming, so don't expect it soon :-(

9) I found a solution, but it doesn't seem correct. Is this a bug ?

No, in fact, the 'Resta' algorithm used in the search tries to divide the temporary sums to reduce the search time.

A recent example:

(6,1,7) 173905-166770-10322-1261-3103-2220-2083-83
(6,1,7) 173905-166770-10322-1261-3103-2083-83-740
(6,1,7) 173905-166770-10322-1261-3103-2220-2083-83
(6,1,7) 173905-166770-10322-1261-3103-2083-83-740

If you check the sums, you can verify that it doesn't sum to zero.

In fact, the solution found is:

173905=166770+130326+93240+87486+72254+26481+3486

And, yes, this solution has been found in four different ways.

(the first decomposition is: 173905-166770-10322*7-1261*21-3103*42-2220*42-2083*42-83*42)

10) I found a bug, what can I do ?

Simply report it to <euler@free.fr>
I need your feedback to locate and fix the bugs, thanks !

For the moment, I'm aware of the following bugs:
 - if you are behind a password protected proxy, Euler2000 won't connect to EulerNet.
 - if the connection to the EulerNet server takes more than 2 minutes, you'll get a message indicating a time-out error.

11) I'm interested in helping, what can I do ?

Firstly, run the client.

Secondly, in finding a relation between all the current known solutions:

34781=33354+24360+21252+19229+18480+10920+8190
38191=34223+33726+16506+12432+9102+7266+6216
39779=37506+31752+22008+17955+12516+11834+2940
54347=48846+46032+33376+32748+19467+3150+2100
59819=51744+48342+44310+42966+9402+8715+7574
63631=54138+54018+48090+39088+25263+23268+1344
66029=58758+51891+51366+38892+25582+20916+12264
67681=65100+49968+35574+33138+32046+8001+2800
70513=60550+57978+57246+26040+21672+18417+13314
78919=75978+57890+40761+38730+38598+26124+13776
89797=83580+67704+60018+58450+27852+11739+10038
97081=86632+81522+69930+37401+31752+21798+20568
108805=94038+85512+81221+75420+65856+53676+17178
123943=111783+106204+73122+66402+29442+12684+6294
125945=116382+87276+85680+82306+81447+62664+41622
127195=113442+101346+99498+60613+14616+9546+7350
130783=120330+100408+85665+83034+72030+65688+29190
141709=122675+114198+112350+79884+75180+52164+24060
144175=131292+114772+107793+41370+16452+11550+6048
145681=134232+123480+67921+56826+56364+28032+25410
152041=147910+107415+81690+58674+41790+34392+30996
172129=155568+147201+107436+68684+46158+41664+38052
173905=166770+130326+93240+87486+72254+26481+3486
177125=159306+142674+127428+101730+94458+17892+12901
185659=173670+134386+130053+117600+70644+51216+3528
194395=172032+164556+140742+80438+72450+25851+18816
194395=176778+147756+133560+124446+121716+80438+70917
198689=177548+170394+130830+94206+39480+38892+36609
201133=189462+161524+103068+99918+31962+20034+9261

12) What practical applications have the minimal equal sums of like powers ?

We are not aware if this problem has a practical application. Currently, their only application is to improve the algorithms to solve such problems. If you find another utility, please mail us !