query: In how many ways can a number be expressed as a sum of squares of two natural numbers?
positive_passages.docid: 1001
positive_passages.text: Number of integer solutions of $x^2 + y^2 = k$
negative_passages.docid: 4194
negative_passages.text: Which integers can be expressed as a sum of squares of two coprime integers?
negative_passages.docid: 144335
negative_passages.text: Sum of three numbers and the sum of their squares: $x^2+y^2+z^2 \geq \frac{1}{3}$ for $x+y+z=1$
negative_passages.docid: 138569
negative_passages.text: Is the “sum of all natural numbers” unique?
negative_passages.docid: 110958
negative_passages.text: How to solve for any given natural number n?
negative_passages.docid: 67332
negative_passages.text: Sum of two squares modulo p
negative_passages.docid: 35066
negative_passages.text: Nature and number of solutions to $xy=x+y$
negative_passages.docid: 134765
negative_passages.text: Is an integer a sum of two rational squares iff it is a sum of two integer squares?
negative_passages.docid: 101835
negative_passages.text: Which rationals can be written as the sum of two rational squares?
negative_passages.docid: 144779
negative_passages.text: The number of ways to represent $(n^2+n)/4$ as a sum of $n/2$ distinct integers in $1,\dots,n$
negative_passages.docid: 57250
negative_passages.text: Proving that the sum and difference of two squares (not equal to zero) can't both be squares.
negative_passages.docid: 35864
negative_passages.text: Playing with numbers form $1$ to $n^2$ in an $n\times n$ grid
negative_passages.docid: 3479
negative_passages.text: How to count the no. of distinct ways in which $1,2,...,6$ can be assigned to $6$ faces of a cube?
negative_passages.docid: 34617
negative_passages.text: Number Theory: which primes are a sum of two squares?
negative_passages.docid: 152638
negative_passages.text: The set of integers $n$ expressible as $n=x^2+xy+y^2$
negative_passages.docid: 119046
negative_passages.text: Expressing a positive integer as a sum of positive integers
negative_passages.docid: 73570
negative_passages.text: Sum of (example: 0+1+2+3 = 6 , 0+1+2+3+4+5+6+7 = 28 and so on)