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TP
1
VM
19 tháng 8 2020
Đặt \(A=12.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(\Rightarrow2A=24.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^2-1\right).\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^4-1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^8-1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^{16}-1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^{16}\right)^2-1^2\)
\(2A=5^{32}-1\)
\(\Rightarrow A=\frac{5^{32}-1}{2}.\)
16 tháng 8 2016
Theo đầu bài ta có:
\(12\cdot\left(5^2+1\right)\cdot\left(5^4+1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)\)
\(=\frac{24}{2}\cdot\left(5^2+1\right)\cdot\left(5^4+1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)\)
\(=\frac{\left(5^2-1\right)\cdot\left(5^2+1\right)\cdot\left(5^4+1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)}{2}\)
\(=\frac{\left(5^4-1\right)\cdot\left(5^4+1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)}{2}\)
\(=\frac{\left(5^8-1\right)\cdot\left(5^8+1\right)\cdot\left(5^{16}+1\right)}{2}\)
\(=\frac{\left(5^{16}-1\right)\cdot\left(5^{16}+1\right)}{2}\)
\(=\frac{5^{32}-1}{2}\)
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
PC
2
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
\(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^{16}-1\right)\left(5^{16}+1\right)\)
\(2P=5^{32}-1\)
\(P=\frac{5^{32}-1}{2}\)