Prove that $2AB$ is square
127566
$2AB$ is a perfect square and $A+B$ is not a perfect square
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
9986
Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $
23048
The ring $\mathbb Z[\sqrt{-2}]= \{a+b\sqrt{-2} ; a\in \mathbb Z,b\in \mathbb Z \}$ has a Euclidean algorithm
86807
The units of $\mathbb Z[\sqrt{2}]$
92106
Prove that $n$ is a sum of two squares?
94570
Proof that every odd integer is a difference of two squares
28781
$k^{2}+(k+1)^{2}$ being a perfect square for infinitely many $k$
136868
Prove that $\sqrt{a^2+3b^2}+\sqrt{b^2+3c^2}+\sqrt{c^2+3a^2}\geq6$ if $(a+b+c)^2(a^2+b^2+c^2)=27$
2771
A group has odd number of elements iff each element is a square, $a=b^2$.
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
93948
Is my proof correct? $p_1p_2p_3\cdots p_n+1)$ cannot be the square of an integer
34906
Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.
87111
Prove $\sqrt{2}$ is between $\dfrac{a}{b}$ and $\dfrac{a+2b}{a+b}$
77081
Proving square root of a square is the same as absolute value
41789
Fermat's theorem on sums of two squares
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$