Question

a^43+b^47=2^2022 Give examples for a and b

Answer 1

Răspuns:

a=2^43

b=2^47

sau reciproc

Explicație pas cu pas:

2021=43*47

si 2^2022=2^2021+2^2021

putem alege

a^43=2^2021=(2^43)^47

b^47=2^2021=(2^47)^43

Indicatie ..nu m-am prins ..decat descompunand pe 2021 care era impar, inprodus de factori primi impari

Answer 2

$\it 2^{2022}=2^{1+2021}=2\cdot2^{2021}=2^{2021}+2^{2021}=\\ \\ =2^{47\cdot43}+2^{43\cdot47}=(2^{47)^{43}}+(2^{43})^{47}\\ \\ Deci,\ (2^{47)^{43}}+(2^{43})^{47}=2^{2022},\ prin\ urmare:\ a=2^{47},\ \ b=2^{43}$