query: The largest number to break a conjecture
positive_passages.docid: 5574
positive_passages.text: Conjectures that have been disproved with extremely large counterexamples?
negative_passages.docid: 32653
negative_passages.text: Smallest integer divisible by all up to $n$
negative_passages.docid: 53670
negative_passages.text: Prove that it is possible to choose $100$ out of the first $200$ positive integers
negative_passages.docid: 132041
negative_passages.text: Numbers which cannot be formed
negative_passages.docid: 48949
negative_passages.text: Solving a Diophantine equation with a large solution
negative_passages.docid: 73345
negative_passages.text: maximum size of a $k$-intersecting family of $[n]$
negative_passages.docid: 114404
negative_passages.text: For which positive integer values of $n$ does $a|mn-b?$
negative_passages.docid: 14783
negative_passages.text: A Number Theory problem (GCD)
negative_passages.docid: 29084
negative_passages.text: Largest integer that can't be represented as a non-negative linear combination of $m, n = mn - m - n$? Why?
negative_passages.docid: 66216
negative_passages.text: Squares, Cubes and Prime numbers
negative_passages.docid: 53231
negative_passages.text: A slightly stronger version of the Goldbach conjecture?
negative_passages.docid: 40896
negative_passages.text: What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$
negative_passages.docid: 118674
negative_passages.text: Simple upper bound for $\binom{n}{k}$
negative_passages.docid: 103581
negative_passages.text: Which positive integers can NOT be written as a sum of consecutive positive integers
negative_passages.docid: 117672
negative_passages.text: finding largest increasing subset of an array (non-contiguous)
negative_passages.docid: 20478
negative_passages.text: Mathematical expression for $n$ largest values in a set
negative_passages.docid: 118443
negative_passages.text: What is the largest $k$ such that $ \frac { k(abc) }{ a+b+c } \le \left( a+b \right) ^{ 2 }+\left( a+b+4c \right) ^{ 2 } $?