query: $\gcd(a+b, p^4)$ if $\gcd(a,p^2) = p$ and $\gcd(b,p^3)=p^2$
positive_passages.docid: 152878
positive_passages.text: calculate the gcd of $a+b$ and $p^4$
negative_passages.docid: 90283
negative_passages.text: Proof that $3 \mid \left( a^2+b^2 \right)$ iff $3 \mid \gcd \left( a,b\right)$
negative_passages.docid: 31465
negative_passages.text: Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
negative_passages.docid: 36
negative_passages.text: Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
negative_passages.docid: 66748
negative_passages.text: Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
negative_passages.docid: 107914
negative_passages.text: Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$
negative_passages.docid: 1713
negative_passages.text: number theory $\gcd(a,bc)=\gcd(a,c)$
negative_passages.docid: 2208
negative_passages.text: $\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
negative_passages.docid: 20003
negative_passages.text: Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer
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: 130653
negative_passages.text: $p^2$ divides $ab$ and $\gcd(a,b)=1$. Show $p^2$ divides $a$ or $p^2$ divides $b$
negative_passages.docid: 73972
negative_passages.text: How to prove that $\gcd(2n^3-14n+2,n+3) = \gcd(n+3,10)$?
negative_passages.docid: 92645
negative_passages.text: Why isn't $\gcd(x^2+3x+2,x^2+x)=(x+1)$? [unit normalization of gcds]
negative_passages.docid: 91506
negative_passages.text: If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
negative_passages.docid: 78678
negative_passages.text: If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
negative_passages.docid: 127993
negative_passages.text: Let $p$ be a prime. Suppose that $\gcd(a, b) = p$. Find $\gcd(a^2,b)$ for all integers $a$ and $b$.
negative_passages.docid: 126280
negative_passages.text: In a P.I.D., if $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$ with $\gcd(m,n) = 1$, then $a=b$