Jump to content
  • Advertisement
Sign in to follow this  
Moe

1782^12 + 1841^12 = 1922^12?

This topic is 4444 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

Hey everyone... For one of my courses at university (Introduction to Linear Algebra) our teacher gave us a challenge. He said if we can prove the following equation right we get a free book on Linear Algebra, and get to describe how we did it in front of the class. He mentioned that it was a problem that was outstanding for quite some time, and that it was only recently solved. The equation (as far as I can tell what it is): 178212 + 184112 = 192212 Now I am not asking for an answer, but what I wouldn't mind is a point in the right direction. Is there a particular name for this problem? I am guessing wikipedia will no doubt have something on it, but seeing as I don't know what it is called, it is a little hard to find. Any ideas/hints/thoughts?

Share this post


Link to post
Share on other sites
Advertisement
I'm not quite sure what you mean by prove it right; they're just numbers, and any calculator will tell you they're the same. What are you meant to be doing?

Share this post


Link to post
Share on other sites
Well, considering the size of the numbers, an average calculator wouldn't be able to do it without at least losing some precision.

Share this post


Link to post
Share on other sites
Quote:
Original post by Moe
178212 + 184112 = 192212


False. Not only because of Fermat's Last Theorem, but easily shown for this example:

178212 must have a units digit the same as that of 212 = 4096.
Similarly, 184112 must have a units digit of 1.

So, the units digit of 178212 + 184112 is 7, but that of 192212 is 6.

Thus the equation is false.

Share this post


Link to post
Share on other sites
If you only need to prove that one equation then write a computer program to just calculate it. Make a special class that stores numbers as arrays of digits 1 to 10 (or you could save space by using bytes and converting all numbers to base 2). So the number 1922 would be an array of size 4 with the digits 1 9 2 and 2.

Then write overloads for addition, mult, and equality.

Course, for your teacher to be completely satisfied, you'll also have to write up some sort of proof that shows your algorithms and class are correct!

Share this post


Link to post
Share on other sites
Quote:
Original post by rpreller
If you only need to prove that one equation then write a computer program to just calculate it. Make a special class that stores numbers as arrays of digits 1 to 10 (or you could save space by using bytes and converting all numbers to base 2). So the number 1922 would be an array of size 4 with the digits 1 9 2 and 2.

Then write overloads for addition, mult, and equality.

Course, for your teacher to be completely satisfied, you'll also have to write up some sort of proof that shows your algorithms and class are correct!


Or use Python!

>>> (1782 ** 12) + (1841 ** 12)
2541210258614589176288669958142428526657L

>>> 1922 ** 12
2541210259314801410819278649643651567616L

Share this post


Link to post
Share on other sites
Heh, I never knew that Python could do such things! I think I will eventually have to learn Python...

bakery2k1: I am not entirely sure that I follow you. What do you mean by "unit digit"?

(Please, forgive my ignorance of math. I haven't taken a math course sinse high school, and that was over 4 years ago [sad]).

Share this post


Link to post
Share on other sites
Sign in to follow this  

  • Advertisement
×

Important Information

By using GameDev.net, you agree to our community Guidelines, Terms of Use, and Privacy Policy.

We are the game development community.

Whether you are an indie, hobbyist, AAA developer, or just trying to learn, GameDev.net is the place for you to learn, share, and connect with the games industry. Learn more About Us or sign up!

Sign me up!