# 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.

## 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 on other sites
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 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 on other sites
Quote:
 Original post by SymphonicIt ain't so

Many thanks and a Rate++ to you, good sir!

##### Share on other sites
Quote:
 Original post by Moe178212 + 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 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.

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 on other sites
Quote:
 Original post by rprellerIf 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 ** 122541210259314801410819278649643651567616L

##### 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 on other sites
he's referring to the last digit of the number (one's place, units place- same thing)

1. 1
Rutin
68
2. 2
3. 3
4. 4
5. 5

• 11
• 11
• 21
• 10
• 33
• ### Forum Statistics

• Total Topics
633438
• Total Posts
3011882
• ### Who's Online (See full list)

There are no registered users currently online

×