Proof that in hyperbola sum of squares of a and b is equal to c.
44349
A geometric reason why the square of the focal length of a hyperbola is equal to the sum of the squares of the axes?
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
92106
Prove that $n$ is a sum of two squares?
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
101832
Proof that sum of first $n$ cubes is always a perfect square
89838
Prove that $3 \le a+b+c \le 2\sqrt{3}$ in a triangle
13466
Prove that if a|b and b|c then a|c using a column proof that has steps in the first column and the reason for the step in the second column.
5729
If $a^2+b^2+c^2=1$ then prove the following.
95852
Prove that $(a+b)(b+c)(c+a) \ge8$
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
127566
$2AB$ is a perfect square and $A+B$ is not a perfect square
80789
Prove that $\forall a,b,c,d\in \mathbb{R}\,$, $(a^2-b^2)(c^2-d^2)\leq(ac-bd)^2$ and equalities hold if and only if $ad=bc$.
13914
If $a^2+b^2=c^2$ then $a$ or $b$ is even.
93685
Erdős's proof of Sylvester's theorem
44621
Simple binomial theorem proof: $\sum_{j=0}^{k} \binom{a+j}j = \binom{a+k+1}k$