Find the least positive integer that can be added to the product of any four consecutive integers such the result is always the square of an integer.
78593
Prove that the product of four consecutive positive integers plus one is a perfect square
75039
Smallest positive element of $ \{ax + by: x,y \in \mathbb{Z}\}$ is $\gcd(a,b)$
135212
The square of an integer has form $3n$ or $3n+1$
108238
Find the smallest integer $n$ greater than $1$ such that the last $3$ digits of $n^2$ are the same as the last $3$ digits of $n$.
47960
Given any $10$ consecutive positive integers , does there exist one integer which is relatively prime to the product of the rest ?
114796
Direct proof that the product of odd integers is odd
126367
Let $p$, $q$ be prime numbers such that $n^{3pq} – n$ is a multiple of $3pq$ for all positive integers $n$. Find the least possible value of $p + q$.
18633
Prove every odd integer is the difference of two squares
1507
The product of $n$ consecutive integers is divisible by $n$ factorial
64052
Among any three consecutive positive integers one is a multiple of 3
115244
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
112644
The product of two numbers that can be written as the sum of two squares
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
45911
Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer
105985
Prove that all even integers $n \neq 2^k$ are expressible as a sum of consecutive positive integers
128387
Given that $a+b\sqrt[3]{2} +c\sqrt[3]{4} =0$, where $a,b,c$ are integers. Show $a=b=c=0$
39156
Concerning what is between two consecutive squares.