• Diofant

$$(a^2-b^2)(c^2-d^2)=(ac+bd)^2-(ad+bc)^2,$$

• Bramagupta

$$(a^2-Nb^2)(c^2-Nd^2)=(ac+Nbd)^2-N(ad+bc)^2,$$

• Aryabhata

$$(1+2+3+\dots +n)^2=1^3+2^3+3^3+\dots +n^3, $$

• Euler

$${\left(1+\frac{1}{3}-\frac{1}{5}-\frac{1}{7}+\frac{1}{9}+\frac{1}{11}-\dots\right)}^2=1+\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+\dots,$$