Every positve integer can be written uniquely as a product of a square and a square-free integer
63182
For every $n \ge 1$ there exist uniquely determined integers $a \gt 0$ and $b \gt 0$ such that $n = a^2b$ where $b$ is square-free.
72389
Positive integer $n$ such that $2n+1$ , $3n+1$ are both perfect squares
121469
Proof of observations on natural numbers being expressed as differences of squares.
63313
Uniqueness of Powerseries in an arbitrarily small neighborhood of $0$ in $\mathbb C$
152638
The set of integers $n$ expressible as $n=x^2+xy+y^2$
144592
how to prove the existence and uniqueness of the prime factorization of any natural number.
23707
How can I prove that every word has unique representation?
16235
Prove by induction that every positive integer is represented by some binary number?
18887
Euclidean domain in which the quotient and remainder are always unique
119046
Expressing a positive integer as a sum of positive integers
48430
Prove the following sequence always results in a perfect square.
138569
Is the “sum of all natural numbers” unique?
57368
Prove that a positive polynomial function can be written as the squares of two polynomial functions
142584
Confusion in proof that primes $p = 4k + 1$ are uniquely the sums of two squares
24561
$\mathbb S_n$ as semidirect product
41726
Musical and combinatorial proof
103581
Which positive integers can NOT be written as a sum of consecutive positive integers