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5^61 + 25^31 + 125^21
= 5^61 + 5^62 + 5^63
= 5^61 x (1+5+25)
= 5^61 x 31 chia hết 31
5^61 + 25^31 + 125^21
= 5^61 + 5^62 + 5^63
= 5^61 x (1+5+25)
= 5^61 x 31 chia hết 31
\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\cdot\cdot\cdot\left(\frac{1}{2009}-1\right)\)
\(=\frac{-1}{2}\cdot\frac{-2}{3}\cdot\cdot\cdot\cdot\frac{-2008}{2009}\)
\(=\frac{\left(-1\right)\cdot\left(-2\right)\cdot\cdot\cdot\left(-2008\right)}{2\cdot3\cdot\cdot\cdot2009}\)
\(=\frac{1\cdot2\cdot\cdot\cdot2008}{2\cdot3\cdot\cdot\cdot2009}\)
\(=\frac{1}{2009}\)
561 + 2531 + 12521 = 561 + (52)31 + (53)21 = 561 + 562 + 563 = 561 + 561 . 5 + 561 . 52 = 561(1 + 5 + 52)
= 561 . 31
có: 155 = 31 . 5
=> 561 . 31 chia hết cho 31 . 5
Ta xét :
\(5^{61}+25^{31}+125^{21}\)
\(=5^{61}+\left(5^2\right)^{31}+\left(5^3\right)^{21}\)
\(=5^{61}+5^{62}+5^{63}\)
\(=5^{61}\left(1+5+25\right)\)
\(=5^{61}.31\)
Vì \(31⋮31\)nên \(5^{61}.31⋮31\)
\(\Rightarrow5^{61}+25^{31}+125^{21}⋮31\)
\(\RightarrowĐPCM\)
5^61+25^31+125^21 =5^61+5^62+5^63 =5^61(1+5+5^2) =5^61.31
Không chia hết cho 3 đâu bạn, chỉ 31 thôi
a) Có: \(4^{51}+2^{104}+4^{53}\\ =4^{51}+\left(2^2\right)^{52}+4^{53}\\ =4^{51}+4^{52}+4^{53}\\ =4^{51}\left(1+4+4^2\right)\\ =4^{51}\cdot21⋮21\left(đpcm\right)\)
b) Có: \(125^{10}+5^{31}+25^{16}\\ =\left(5^3\right)^{10}+5^{31}+\left(5^2\right)^{16}\\ =5^{30}+5^{31}+5^{32}\\ =5^{30}\left(1+5+5^2\right)\\ =5^{30}\cdot31⋮31\left(đpcm\right)\)
c) Có: \(2^{25}+4^{13}+8^9\\ =2^{25}+\left(2^2\right)^{13}+\left(2^3\right)^9\\ =2^{25}+2^{26}+2^{27}\\ =2^{23}\left(2^2+2^3+2^4\right)\\ =2^{23}\cdot28⋮28\left(đpcm\right)\)
Ta có: \(27^{20}+3^{61}+9^{31}\)
\(=\left(3^3\right)^{20}+3^{61}+\left(3^2\right)^{31}\)
\(=3^{60}+3^{61}+3^{62}\)
\(=3^{60}.\left(1+3+3^2\right)\)
\(=3^{60}.13\)
Vì \(13⋮13\) nên \(3^{60}.13⋮13.\)
\(\Rightarrow27^{20}+3^{61}+9^{31}⋮13\left(đpcm\right).\)
Chúc bạn học tốt!
\(5^{61}+25^{31}+125^{21}=5^{61}+5^{62}+5^{63}\)
\(=5^{61}\left(1+5+5^2\right)=5^{61}.31\)
Chia het cho 31