query: Prove that a given expression is always an integer
positive_passages.docid: 14815
positive_passages.text: How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer
negative_passages.docid: 146439
negative_passages.text: Is every sufficiently large positive integer of the form $ab + ac + bc + 1$?
negative_passages.docid: 39921
negative_passages.text: show that f is constant on I
negative_passages.docid: 56760
negative_passages.text: Prove by induction that an expression is divisible by 11
negative_passages.docid: 114100
negative_passages.text: Why do I get "integer expression required"?
negative_passages.docid: 92057
negative_passages.text: Prove that for every odd integer n, there is a group...
negative_passages.docid: 69439
negative_passages.text: Infinite Sum of algebraic expression
negative_passages.docid: 87425
negative_passages.text: Prove that if $A$ is a square matrix with integer entries and $\det(A) = \pm 1$, then $A^{-1}$ contains all integer entries.
negative_passages.docid: 84558
negative_passages.text: Prove that the square root of a positive integer is either an integer or irrational
negative_passages.docid: 10905
negative_passages.text: Avoiding negative integers in proof of Fundamental Theorem of Arithmetic
negative_passages.docid: 145397
negative_passages.text: How to prove that for every $i$, $a_i = i$
negative_passages.docid: 137718
negative_passages.text: Prove that the complex expression is real
negative_passages.docid: 63804
negative_passages.text: Proof that every repeating decimal is rational
negative_passages.docid: 134
negative_passages.text: Prove that the expression is a perfect square
negative_passages.docid: 20438
negative_passages.text: Prove that every positive integer $n$ has a unique expression of the form: $2^{r}m$ where $r\ge 0$ and $m$ is an odd positive integer
negative_passages.docid: 141227
negative_passages.text: How to show the integers have same cardinality as the natural numbers?
negative_passages.docid: 123195
negative_passages.text: Prove by induction that a^n+a^-n is an integer.