query: If $a\mid b^2$ and $\gcd(a,b) = 1$, how can I prove that $a\mid b$?
positive_passages.docid: 37596
positive_passages.text: If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
negative_passages.docid: 7316
negative_passages.text: How to prove that $z\gcd(a,b)=\gcd(za,zb)$
negative_passages.docid: 83307
negative_passages.text: If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
negative_passages.docid: 69967
negative_passages.text: How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?
negative_passages.docid: 72424
negative_passages.text: Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1
negative_passages.docid: 1713
negative_passages.text: number theory $\gcd(a,bc)=\gcd(a,c)$
negative_passages.docid: 55441
negative_passages.text: Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
negative_passages.docid: 19700
negative_passages.text: Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$
negative_passages.docid: 25573
negative_passages.text: If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
negative_passages.docid: 6012
negative_passages.text: Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
negative_passages.docid: 157784
negative_passages.text: Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
negative_passages.docid: 52930
negative_passages.text: Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
negative_passages.docid: 56612
negative_passages.text: Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
negative_passages.docid: 40848
negative_passages.text: $a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
negative_passages.docid: 34330
negative_passages.text: How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
negative_passages.docid: 113641
negative_passages.text: Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
negative_passages.docid: 77064
negative_passages.text: Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$