If a nine digit number is formed by the nine non zero digits with units digit $5$, prove that it must not be a perfect square.
140155
Proving that a number with digits 1...9 in some order, ending in 5, is not a perfect square.
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
36011
Show that the product of two consecutive natural numbers is never a square.
46102
Prove that $2^n +1$ in never a perfect cube
24601
Proving that a natural number made entirely of 6's and 0's is not a square.
72437
Sum of the digits of a perfect square
19588
$n!+1$ being a perfect square
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
155784
If $\gcd(a, b) = 1$ and if $ab = x^2$, prove that $a, b$ must also be perfect squares; where $a,b,x$ are in the set of natural numbers
117380
Divisibility Rule for 9
99606
Prove or disprove there exists a set of four numbers out of the $48$ positive integers of which product is a perfect square
68903
The number $2^{29}$ has exactly $9$ distinct digits. Which digit is missing?
154494
Prove that there exists a row or a column of the chessboard which contains at least √n distinct numbers.
45911
Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer
127566
$2AB$ is a perfect square and $A+B$ is not a perfect square
59261
If $n\in\Bbb Z^+$ is not a square, prove exist infinitely many primes $p$ such that $\left(\frac{n}{p}\right)=-1$.
110722
$n$ and $n^5$ have the same units digit?