Prove that MCD is 1 or 3 knowing (a,b) = 1
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
95935
Prove A = $(A \cap B) \cup (A \cap B^c)$ using the distributive and associative law.
136459
Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$
116215
Prove that $P(A \cap B\mid C)=P(A \mid (B \cap C))P(B\mid C)$
155545
Showing that $a \mid b$ and $b \mid a$ if and only if $a= \pm b$.
64108
how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
119964
Prove: $1/2(a+b) \times (a - b) = b \times a$ - in three space
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.