Show that, in all bases $n$ greater than $3$, the number written as $1331$ is a perfect cube.
88350
Prove that the number 14641 is the fourth power of an integer in any base greater than 6?
96737
Geometric proof that a Pythagorean triple has a number divisible by $3$?
84220
Questions on perfect squares
92057
Prove that for every odd integer n, there is a group...
138548
For what pair of integers $(a,b)$ is $3^a + 7^b$ a perfect square.
16660
Prove that any positive number has an $n$th root
35326
There are infinitely many $N$ such that $\frac{N}{2}$ is a perfect square, $\frac{N}{3}$ is a perfect cube, and $\frac{N}{5}$ is a perfect fifth power
41641
$(n-7)(n+7)=$ some perfect square
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
66358
Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
5692
Proving that there is a perfect square between $n$ and $2n$
24446
Prove that for each $n$, there exist $n$ consecutive integers, each of which is divisible by a perfect square larger than $1$.
99606
Prove or disprove there exists a set of four numbers out of the $48$ positive integers of which product is a perfect square
156319
Show that a group with $|G| = 33$ contains an element of order $3$
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.
72389
Positive integer $n$ such that $2n+1$ , $3n+1$ are both perfect squares
125401
Mathematical Induction: Sum of first n odd perfect cubes