If $a,b,c$ and $d$ non-zero natural number such that $ab=cd$
29799
Sum of four squares not a prime
111800
If $a|c$ and $b|d$, is it true that $ab|cd$?
96630
Let a and b be real numbers such that 0  \sqrt{ab} > \frac{2ab}{a + b}$
48051
Proof related to natural numbers
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
101159
Prove If a ≡ b (mod n) and c ≡ d (mod n), then a + c ≡ b + d (mod n)
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
124320
$a,b,c>0 \text{ s.t. }a+b+c=1 \implies \sqrt{ab+c}+\sqrt{bc+a}+\sqrt{ca+b} \ge 1+ \sqrt{ab}+\sqrt{bc}+\sqrt{ca}$
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
104124
Prove or disprove: $A-(B-C) = (A-B)-C$
17677
Prove or show a counter example for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$
149269
If $a,b,c,d,e,f$ are non negative real numbers such that $a+b+c+d+e+f=1$, then find maximum value of $ab+bc+cd+de+ef$