word problem

• Apr 16th 2008, 07:35 AM
hotgal24
word problem
• Apr 16th 2008, 08:01 AM
Isomorphism
I claim 103138 divides that number for all positive integer values of n.

This is done by observing that \$\displaystyle a-b\$ divides \$\displaystyle a^n - b^n\$ and then rearranging the given number into sums of such differences.

For example,

\$\displaystyle 278 = 2141-1863\$ and \$\displaystyle -278 = 1492 - 1770\$

Thus \$\displaystyle 278|2141^n -1863^n + 1492^n - 1770^n\$

Similarly \$\displaystyle 371 = 2141 - 1770\$ and \$\displaystyle -371 = 1492 - 1863\$

Thus \$\displaystyle 371|2141^n -1863^n + 1492^n - 1770^n\$

Since (371,278) = 1

\$\displaystyle (371)(278) = 103138|2141^n -1863^n + 1492^n - 1770^n\$
• Apr 16th 2008, 04:58 PM
topsquark
Quote:

Originally Posted by Isomorphism
I claim 103138 divides that number for all positive integer values of n.

So the year 103,138 is the end of the world??? (Crying)

On second thought, I'm not going to worry about that too much. (Sleepy)

-Dan
• Apr 16th 2008, 07:18 PM
Isomorphism
Quote:

Originally Posted by topsquark
So the year 103,138 is the end of the world??? (Crying)

On second thought, I'm not going to worry about that too much. (Sleepy)

-Dan

According to the article that means this fact will be discovered on April 1,103138. Which means at least until then we have no End of the World (Rofl)
• Apr 16th 2008, 07:24 PM
angel.white
You don't have to solicit help on this forum, most people are more than happy to answer questions, even if they aren't winning a date with a "hot gal" and even if it doesn't prove they're a "REAL GENIUS"