query: if |x -4 | + |y - 4| =4 then how many integers value is possible for the set (x,y)
positive_passages.docid: 150152
positive_passages.text: If $|x -4 | + |y - 4| =4$ then how many integers value the sets (x,y) have?
negative_passages.docid: 93572
negative_passages.text: How to determine if $n (n \geq 2)$ given numbers can be summed up to a certain number?
negative_passages.docid: 33735
negative_passages.text: The square of an integer is congruent to 0 or 1 mod 4
negative_passages.docid: 74713
negative_passages.text: Show that for any natural numbers, if $S(x)=S(y)$ then $x=y$.
negative_passages.docid: 102349
negative_passages.text: sum of all the numbers that can be formed using the digits 2,3,3,4,4,4..
negative_passages.docid: 117392
negative_passages.text: Does $x^2 - y^2 = 12345678$ (x,y are integers) have any solutions?
negative_passages.docid: 133937
negative_passages.text: Find the four digit number?
negative_passages.docid: 137010
negative_passages.text: What are integers $x$ and $n$ such as $ x^4+x^3+x^2+x+1 = n^2$?
negative_passages.docid: 87846
negative_passages.text: If $\gcd (x,4) = 2$ and $\gcd(y,4) = 2$ then $\gcd(x+y,4) = 4$
negative_passages.docid: 108275
negative_passages.text: How do I count the subsets of a set whose number of elements is divisible by 3? 4?
negative_passages.docid: 86285
negative_passages.text: Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
negative_passages.docid: 34784
negative_passages.text: Is a number meeting these conditions divisible by forty-nine?
negative_passages.docid: 48502
negative_passages.text: number of ordered pairs of integers $(x,y)$ satisfying the equation
negative_passages.docid: 17703
negative_passages.text: $S$ be a collection of subsets of $\{1,...,100\}$ ; any two sets in $S$ has non-empty intersection , what is the maximum possible value of $|S|$?
negative_passages.docid: 15753
negative_passages.text: Solve the following equation in positive integers $x$ and $y$
negative_passages.docid: 141227
negative_passages.text: How to show the integers have same cardinality as the natural numbers?
negative_passages.docid: 11750
negative_passages.text: Prove that n is divisible by 4 in a cylic sum with variables which have only two possible values