Question

care poate fi ultima cifra a numărului 2n+1 stind ca este pătrat perfect? ​

Answer 1

$\displaystyle\it\\un~patrat~perfect~poate~fi~de~forma: \mathcal{M}_{10},\mathcal{M}_{10}+ 1, \mathcal{M}_{10}+4, \\\mathcal{M}_{10}+5,\mathcal{M}_{10}+ 6,\mathcal{M}_{10}+ 9.\\2n=\mathcal{M}_{10},\mathcal{M}_{10}+2,\mathcal{M}_{10}+4,\mathcal{M}_{10}+6,\mathcal{M}_{10}+8 |+1 \implies\\2n+1=\mathcal{M}_{10}+1,\mathcal{M}_{10}+3,\mathcal{M}_{10}+5,\mathcal{M}_{10}+7,\mathcal{M}_{10}+9 \implies\\2n+1~cand~este~patrat~perfect,~are~formele:$

$\displaystyle\it\\\mathcal{M}_{10}+1,~\mathcal{M}_{10}+5,\mathcal{M}_{10}+9$