How to show that $\log_{10} n$ is not a rational number if $n$ is any integer not a power of $10.$
15110
About irrational logarithms
119545
Nonzero rationals under multiplication are not a cyclic group
32516
show that rational numbers with the multipiciation are not abelian finitely generated group
1570
Show that log $Fib_{n}$ is $\theta(n)$
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
56464
Proving the irrationality of $e^n$
76032
Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5
36011
Show that the product of two consecutive natural numbers is never a square.
149758
How to prove $\log n < n$?
100037
nth roots and logarithm
82485
Show that the set of non zero rationals is not a cyclic group under multiplication.
32
Is $n^{th}$ root of $2$ an irrational number?
63300
Product of Consecutive Integers is Not a Power
24601
Proving that a natural number made entirely of 6's and 0's is not a square.
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
70523
Proving that $x^4 - 10x^2 + 1$ is not irreducible over $\mathbb{Z}_p$ for any prime $p$.
148035
Is it possible for a sequence of rational numbers to have a non rational limit?