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Xét: 215 = 23 . 23 . 23 . 23 . 23 = 8.8.8.8.8 = (.....4).(.....4) . 8 = (....8)
Xét: \(3^{15}=3^5.3^5.3^5=\left(...3\right)\left(...3\right)\left(....3\right)=\left(....7\right)\)
Xét: \(5^2=25\)
Vậy \(2^{15}+3^{15}+5^2=\left(......8\right)+\left(.....7\right)+25=\left(.....0\right)\) chia hết cho 5
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Ta có: \(2^{4n}-1=\left(2^4\right)^n-1⋮2^4-1\Rightarrow2^{4n}-1⋮15\)
\(2^{4n}-1=\left(2^4\right)^n-1^n=\left(2^4-1\right)\left[\left(2^4\right)^{n-1}+...+1\right]=15M\) .Vậy \(2^{4n}-1⋮15\)
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A=3n(n^2+674)
TH1: n=3k
=>A=3*3k(n^2+674)=9k(n^2+674) chia hết cho 9
TH2: n=3k+1
=>A=3(3k+1)(9k^2+6k+1+674)
=3(3k+1)(9k^2+6k+675)
=9(3k+1)(3k^2+2k+225) chia hết cho 9
TH3: n=3k+2
=>A=3(3k+2)(9k^2+12k+4+674)
=3(3k+2)(9k^2+12k+678)
=9(3k+2)(3k^2+4k+226) chia hết cho 9
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\(3^{15}+3^{16}+3^{17}\)
\(=3^{15}\left(1+3+9\right)\)
\(=3^{15}.13\)
\(\Rightarrow3^{15}\times13⋮3\)
Vậy \(3^{15}+3^{16}+3^{17}⋮3\)
=15^2020(1+15^2)
=226*15^2020 chia hết cho 226