Question

aratati ca 5^2020+2021^5 nu este patrat perfect​

Answer 1

$\displaystyle\it\\folosim~proprietatea~:~\boxed{\it (a+b)^n=\mathcal{M}_{a}+b^n}~.\\un~patrat~perfect~poate~avea~una~din~formele~:~\mathcal{M}_4,~\mathcal{M}_4+1\\---------------------\\5^{2020}+2021^{5}=(4+1)^{2020}+(2020+1)^{5}=\\\mathcal{M}_{4}+1^{2020}+\mathcal{M}_{4}+1^{5}= \mathcal{M}_{4}+2,~dar~un~~patrat~perfect\\nu~poate~fi~de~forma~\mathcal{M}_{4}+2,~prin~urmare~numarul~nu\\este~un~patrat~perfect.$