Prove if the remainder is relatively prime to the divisor, the dividend is also relatively prime to the divisor and vice versa?
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
116585
$r$ primitive root of prime $p$, where $p \equiv 1 \mod 4$: prove $-r$ is also a primitive root
140412
If $p$ and $q$ are distinct primes such that $p|c$ and $q|c$, prove that $pq|c$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
102420
How to prove that adding $n$ to the numerator and denominator will move the resultant fraction close to $1$?
135682
Are distinct prime ideals in a ring always coprime? If not, then when are they?
139776
Divisibility tests and remainder mod $9,11,99,101,999,1001\,$ (casting out nines and elevens)
24098
Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$
43567
Some hints for "If a prime $p = n^2+5$, then $p\equiv 1\mod 10$ or $p\equiv 9\mod 10$"
101385
Congruent iff Same Remainder (CISR) Confusion
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
32343
Converse to Chinese Remainder Theorem
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
10966
gcd and lcm from prime factorization proof
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.