Toán Lớp 7: Chứng tỏ : 5 ^53 – 5 ^52 + 5 ^51 chia hết cho 21
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Toán Lớp 7: Chứng tỏ : 5 ^53 – 5 ^52 + 5 ^51 chia hết cho 21
Comments ( 2 )
#Luân
Ta có
$5^{33}$-$5^{22}$+$5^{51}$
=$5^{21}$($5^{2}$-5+1)
=$5^{21}$(25-5+1)
=$5^{21}$.21
Vì 21$\vdots$21=>$5^{21}$.21$\vdots$21
=>$5^{33}$-$5^{22}$+$5^{51}$$\vdots$21
Chúc bạn học tốt~
$\text{ @HV }$
5^{53} – 5^{52} + 5^{51}
= 5^{51}. (5^2 – 5^1 + 1)
= 5^{51}. (25 – 5 + 1)
= 5^{51}. 21
Mà 21 \vdots 21
⇒ 5^{51}. 21 \vdots 21
Hay 5^{53} – 5^{52} + 5^{51} \vdots 21 (đpcm)