$\underline{\underline{\text{A.}}}a=2\cdot 1+1=2+1=3$  

$b=2\cdot 1\cdot \left(1+1\right)=2\cdot 1\cdot 2=4$  

$c=2\cdot 1\cdot \left(1+1\right)+1=2\cdot 1\cdot 2+1=4+1=5$  

$3^2+4^2\stackrel{?}{=}{5}^2$  

$9+16=25$  

$\underline{\underline{\text{B.}}}a=2\cdot 2+1=5$  

$b=2\cdot 2\cdot \left(2+1\right)=4\cdot 3=12$  

$c=2\cdot 2\cdot \left(2+1\right)+1=4\cdot 3+1=13$  

$5^2+{12}^2\stackrel{?}{=}{13}^2$  

$25+144=169$  

$\underline{\underline{\text{C.}}}a=2\cdot 3+1=6+1=7$  

$b=2\cdot 3\cdot \left(3+1\right)=6\cdot 4=24$  

$c=2\cdot 3\cdot \left(3+1\right)+1=6\cdot 4+1=25$  

$7^2+{24}^2\stackrel{?}{=}{25}^2$  

$49+576=625$  

$\text{D.}a=2\cdot 2+1=4+1=5$  

$b=2\cdot 2\cdot 2+1=8+1=9$  

$c=2\cdot 2\cdot 2\cdot 2+1=16+1=17$  

$5^2+9^2\stackrel{?}{=}{17}^2$  

$25+81\ne 289$  

$\underline{\underline{\text{E.}}}a=2\cdot 4+1=8+1=9$  

$b=2\cdot 4\cdot \left(4+1\right)=8\cdot 5=40$  

$c=2\cdot 4\cdot \left(4+1\right)+1=8\cdot 5+1=40+1=41$  

$9^2+{40}^2\stackrel{?}{=}{41}^2$  

$81+1600=1681$  

$\underline{\underline{\text{F.}}}{\left(2n+1\right)}^2+{\left(2n\left(n+1\right)\right)}^2\stackrel{?}{=}{\left(2n\left(n+1\right)+1\right)}^2$

${\left(2n\right)}^2+2\cdot 2n\cdot 1+1^2+{\left(2n\right)}^2\cdot {\left(n+1\right)}^2\stackrel{?}{=}{\left(2n\left(n+1\right)\right)}^2+2\cdot 2n\left(n+1\right)\cdot 1+1^2$   

$4n^2+4n+1+4n^2\cdot \left(n^2+2n+1\right)\stackrel{?}{=}{\left(2n\right)}^2\cdot {\left(n+1\right)}^2+4n\left(n+1\right)+1$  

$\underline{4n^2+4n+1}+\underline{\underline{4n^2\cdot \left(n^2+2n+1\right)}}=\underline{\underline{4n^2\cdot \left(n^2+2n+1\right)}}+\underline{4n^2+4n+1}$  

Odpowiedź:

A, B, C, E, F