Question

se considera a=2 la 2024 - 4096 la 2.Demonstrsti ca a se divide cu 1024​

Answer 1

Răspuns:

a = 2²⁰²⁴ - 4096²

= 2¹⁰ₓ2²⁰¹⁴ - (4ₓ1024)²

= 1024ₓ2²⁰¹⁴ - 4²ₓ1024²

= 1024(2²⁰¹⁴ - 2⁴ₓ1024) divizibil cu 1024

Answer 2

Explicație pas cu pas:

1024 = 2¹⁰

$\large \bf A = {2}^{2024} - 4096^{2}$

$\large \bf A ={2}^{2024} -( 2^{12})^{2}$

$\large \bf A ={2}^{2024} -2^{12 \cdot2}$

$\large \bf A ={2}^{2024} -2^{24}$

$\large \bf A = {2}^{10} \cdot ({2}^{2024 - 10} -2^{24 - 10} )$

$\large \bf A= {2}^{10} \cdot ({2}^{2014} -2^{14} )$

$\large \bf A = 1024 \cdot ({2}^{2014} -2^{14} ) \implies \boxed{ \bf \: A \: \vdots \: 1024}$

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