1, CMR : 23^401 + 38^202 - 2^433 chia hết cho 5
2, CMR: 9^2014 +3^2013 +2^2012 chia hết cho 10
3, CMR : 3^2013 + 2^2013 chia hết cho 5
1, CMR : 23^401 + 38^202 - 2^433 chia hết cho 5
2, CMR: 9^2014 +3^2013 +2^2012 chia hết cho 10
3, CMR : 3^2013 + 2^2013 chia hết cho 5
1) \(23^{401}+38^{202}-2^{433}=23^{4.100}.23+38^{4.50}.38^2-2^{4.108}.2^1=\left(..1\right).23+\left(..6\right).1444-\left(..6\right).2=\left(..3\right)+\left(..4\right)-\left(..2\right)=\left(..5\right)\)
Cmr 10^2010-1 chia het cho 99
3^1930+2^1930 chia het cho 13
(2^10+1)^2010 chia het cho 25^2010
(30^4)^1975×15^1870×4^935-(7^5)^1954. Chia hết cho 23
12^2000-2^1000 chia hết cho 10
2011^2013+2013^2011 chia het cho 2012
CMR :a)(2^4n-1) chia hết cho 5
b)(9^2n+1) chia hết cho 5 c) (2011^2012+2013^2014) chia hết cho 2
d)(2003^2007+2007^2003) chia hết cho 2;5
Cho x,y,z thuộc Z và P=(x+2012)5+(2y-2013)5+(3z+2014)5; S=x+2y+3z+2013
CMR: P chia hết cho 3 tương đương S chia hết cho 3
CMR : n3 + 5n chia hết cho 6
CTR : (n + 2012)2013 nhân (n + 2013)2012 chia hết cho 2
CMR : n2 + n + 6 chia hết cho 2
CMR 1 .3 .5 ...2013 . 2015 + 2 .4 .6....2014 . 2016 chia hết cho 9911
cho B=1.2.3.4.....2012.(1+1\2+1\3+...+1\2012.CMR B chia hết cho 2013
Cho B = 1.2.3.4.5......2012 .(1+1/2+1/3+...1/2012)
CMR B chia hết cho 2013
CMR: A=3 + 3^2 + 3^3 + .... + 3^2012 + 3^2013 CHIA HẾT CHO 13
\(A=3+3^2+3^3+...+3^{2012}+3^{2013}\)
\(=\left(3+3^2+3^3\right)+...+\left(3^{2011}+3^{2012}+3^{2013}\right)\)
\(=3\left(1+3+3^2\right)+...+3^{2011}\left(1+3+3^2\right)\)
\(=\left(1+3+3^2\right)\left(3+...+3^{2011}\right)\)
\(=13\left(3+...+3^{2011}\right)\)
Vì 13 chia hết cho 13 nên \(13\left(3+...+3^{2011}\right)\) chia hết cho 13
Vậy A chia hết cho 13
A=(3+32+33)+(34+35+36)+...+(32011+32012+32013)
A=3(1+3+32)+34(1+3+32)+...+32011(1+3+32)
A=3.13+3^4.13+...+3^2011.13
A=13(3+3^4+...+3^2011)chia hết cho 13
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