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- Apr 16th 2008, 07:35 AMhotgal24word problem
- Apr 16th 2008, 08:01 AMIsomorphism
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 PMtopsquark
- Apr 16th 2008, 07:18 PMIsomorphism
- Apr 16th 2008, 07:24 PMangel.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"