Tagged Questions
5
votes
1answer
51 views
Does this have a name: If an odd prime $p$ does not divide $a$, then $p$ divides $a^n + 1$ or $a^n - 1$
After seeing and doing a bunch of proofs like "For all $a$ in the natural numbers, then if $7$ does not divide $a$, then $7$ divides $a^3+1$ or $a^3-1$," I conjectured the following, but got stuck in ...
1
vote
1answer
66 views
Looking for references on results on powers of primes dividing $y^n-1$
For a prime $p$ and positive integer $n$,
let $E(n,p)$ be the greatest $k$ such that
$p^k \mid n$, and $E(n,p) = 0$ if $p \nmid n$.
Let $E(n) = E(n, 2)$.
A number of years back,
I proved the ...
3
votes
1answer
127 views
Good resource of maths problems with solutions
I'm searching for a good book or web page that has a good amount of problems and their solutions, at undergraduate level, of divisibility, inequalities, induction, etc.
Thanks in advance
