query: Proof verification: elementary Number Theory Proof of $am+bn = 1$
positive_passages.docid: 44076
positive_passages.text: Proving if $d_0$ is the smallest positive integer in $S$ then $d_0 = \gcd(a,b)$
negative_passages.docid: 14162
negative_passages.text: How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
negative_passages.docid: 121469
negative_passages.text: Proof of observations on natural numbers being expressed as differences of squares.
negative_passages.docid: 84417
negative_passages.text: Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
negative_passages.docid: 7083
negative_passages.text: Alternating sum of binomial coefficients: given $n \in \mathbb N$, prove $\sum^n_{k=0}(-1)^k {n \choose k} = 0$
negative_passages.docid: 70827
negative_passages.text: Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
negative_passages.docid: 133181
negative_passages.text: Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
negative_passages.docid: 76368
negative_passages.text: Proving the Binomial theorem
negative_passages.docid: 153647
negative_passages.text: Elementary number theory and quadratic
negative_passages.docid: 35897
negative_passages.text: Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
negative_passages.docid: 102133
negative_passages.text: Prove: $\gcd(a,b) = \gcd(a, b + at)$.
negative_passages.docid: 141369
negative_passages.text: If $a+b\equiv0\pmod m$ and $c+d\equiv 0\pmod m$ then $ac\equiv bd\pmod m$. Demonstration.
negative_passages.docid: 89175
negative_passages.text: Proof of $(a+b)^{n+1}$
negative_passages.docid: 133905
negative_passages.text: Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
negative_passages.docid: 74631
negative_passages.text: For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
negative_passages.docid: 77164
negative_passages.text: If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
negative_passages.docid: 50266
negative_passages.text: In the following figure prove that: $AK||BC$