0

I think we use induction with base case, $n=7$.

But then what?

Bill Dubuque
  • 272,048
Paul
  • 81
  • Previous comment beat me to it, which is why I am commenting rather than answering. To put it simply, since $3^n$ is odd, $n$ must be odd. Easy to show, by experimenting with small odd positive integers to find the pattern, that when $n$ is an odd positive integer, and $x,y$ are positive integers, $(x+y)|(x^n + y^n).$ – user2661923 Feb 27 '21 at 09:16
  • 1
    @DietrichBurde Interesting comment. If one of the duplicates shows as a suggested query to research before posting, then I think you have a point. If not, then it may be asking a lot, to ask a fairly new user, who might not be adept at determining which keywords to search on, to first spend time checking if the query is a dup. Of all the problems that users have posting queries that are defective in one way or another, failure to aggressively search for dups seems relatively minor. – user2661923 Feb 27 '21 at 09:22
  • @DietrichBurde For example, in this query, the user showed no work, gave no indication of the theorems or previously solved problems that may be relevant, and gave no indication of his math education - skill level - sophistication. – user2661923 Feb 27 '21 at 09:25
  • Sometimes it is really easy to find a duplicate, even if you don't have much experience. I mean, a poster should at least think of trying to search. This is, what I wanted to say. Often the people showing no work here also show no effort about searching. For others, it is sometimes a surprise if they see how easy it is to find a duplicate. For this site it would be much better if the popular questions (with very many answers) are not asked again and again. – Dietrich Burde Feb 27 '21 at 09:26
  • @DietrichBurde I updated the dupe link to one having a simpler and more general proof (btw, it would be a good idea to delete your misleading comment there). – Bill Dubuque Feb 27 '21 at 11:08

0 Answers0