query: four different integers exist, what is the least product value?
positive_passages.docid: 153241
positive_passages.text: Four different positive integers a, b, c, and d are such that $a^2 + b^2 = c^2 + d^2$
negative_passages.docid: 138271
negative_passages.text: Find the least number which when divided by 2, 3, 4, 5, 6 leaves a remainder of 1 but it is divided by 7 completely.
negative_passages.docid: 136763
negative_passages.text: What are the possible integer values for $x,y,z$ if $792|\overline{5x36y98z2}$?
negative_passages.docid: 3208
negative_passages.text: There is no smallest rational number greater than 2
negative_passages.docid: 27428
negative_passages.text: Divisibility test for $4$
negative_passages.docid: 81217
negative_passages.text: Fastest way to find out minimum of 3 numbers?
negative_passages.docid: 143274
negative_passages.text: What is the smallest unknown natural number?
negative_passages.docid: 76330
negative_passages.text: Maximum and Minimum values for ints
negative_passages.docid: 78593
negative_passages.text: Prove that the product of four consecutive positive integers plus one is a perfect square
negative_passages.docid: 3694
negative_passages.text: Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$
negative_passages.docid: 134352
negative_passages.text: The number of possible factorizations of a positive integer.
negative_passages.docid: 60965
negative_passages.text: Representing a nonnegative integer as the ordered sum of odd numbers
negative_passages.docid: 55199
negative_passages.text: Number Theory in a Choice-less World
negative_passages.docid: 56808
negative_passages.text: Getting the lowest and highest value from integers without using arrays?
negative_passages.docid: 153831
negative_passages.text: Approximating $\pi$ with least digits
negative_passages.docid: 126367
negative_passages.text: 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 $p + q$.
negative_passages.docid: 152506
negative_passages.text: The greatest common divisor is the smallest positive linear combination