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VM
19 tháng 8 2020
Đặt \(A=12.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(\Rightarrow2A=24.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^2-1\right).\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^4-1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^8-1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^{16}-1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^{16}\right)^2-1^2\)
\(2A=5^{32}-1\)
\(\Rightarrow A=\frac{5^{32}-1}{2}.\)
BB
0
MA
0
TM
1
DK
13 tháng 9 2017
Nhân cả 2 vế với 2 ta có:
2P=24(52+1)(54+1)(58+1)(516+1)
2P=(52_1)(52+1)(54+1)(58+1)(516+1)
2P=(54_1)(54+1)(58+1)(516+1)
2P=(58_1)(58+1)(516+1)
2P=(516_1)(516+1)
2P=532_1
P=\(\frac{5^{32}-1}{2}\)
DH
0
29 tháng 8 2015
P = 12 ( 52 + 1 ) ( 54 + 1 ) ( 58 +1 ) ( 516 +1 )
=>2P=24 ( 52 + 1 ) ( 54 + 1 ) ( 58 +1 ) ( 516 +1 )
=( 52 - 1 ) ( 52 + 1 ) ( 54 + 1 ) ( 58 +1 ) ( 516 +1 )
=( 54 - 1 ) ( 54 + 1 ) ( 58 +1 ) ( 516 +1 )
=( 58 - 1 ) ( 58 +1 ) ( 516 +1 )
=( 516 - 1 ) ( 516 + 1 )
= 532 - 1
=>P=\(\frac{5^{32}-1}{2}\)
F
4 tháng 10 2020
\(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^{16}-1\right)\left(5^{16}+1\right)\)
\(2P=5^{32}-1\)
\(P=\frac{5^{32}-1}{2}\)
WL
1
10 tháng 9 2015
P=12(5^2+1)(5^4+1)(5^8+1)(5^16+1)
2P=24(5^2+1)(5^4+1)(5^8+1)(5^16+1)
2P=(5-1)(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)
2P=(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)
2P=(5^4-1)(5^4+1)(5^8+1)(5^16+1)
2P=(5^8-1)(5^8+1)(5^16+1)
2P=(5^16-1)(5^16+1)
2P=5^32-1
P=(5^32-1):2
2G
1
DE
14 tháng 8 2019
\(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^{32}+1\right)\)
SL
1
5 tháng 7 2016
\(\left(5^2-1\right)P=12\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(24P=12\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(24P=12\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(24P=12\left(5^{16}-1\right)\left(5^{16}+1\right)\)
\(24P=12\left(5^{32}-1\right)\)
\(P=\frac{12.\left(5^{32}-1\right)}{24}=\frac{5^{32}-1}{2}\)
T I C K nha cảm ơn
\(2P=24\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)=\left(5^{16}-1\right)\left(5^{16}+1\right)=5^{32}-1\Rightarrow P=\frac{5^{32}-1}{2}\)
\(P=12(5^2+1)(5^4+1)(5^8+1)(5^16+1)\)
\(12P=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(12P=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
12P=...
12P=\(\left(5^{16}-1\right)\left(5^{16}+1\right)\)
12P=\(5^{32}-1\)
=>P=\(\dfrac{244140624}{12}=203450552\)
Chú ý rằng 12=24/2=(5^2-1)/2.Vậy
12(5^2+1)(5^4+1)(5^8+1)(5^16+1)=
(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)/2...
(5^4-1)(5^4+1)(5^8+1)(5^16+1)/2=
(5^8-1)(5^8+1)(5^16+1)/2=
(5^16-1)(5^16+1)/2=(5^32-1)/2.
Tất cả các bước đều áp dụng hằng đẳng thức (a+b)(a-b)=a^2-b^2.
Cái này phải bằng \(\frac{5^{32}-1}{2}\)
bạn tính lại nhé!