cho 75 số có tính chất :tích của 3 số bất kì trong chúng là số âm .Hỏi tích của 75 số đó mang dấu gì ?
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Ta có A = 21 + 22 + 23 + ... + 220110
= ( 21 + 22 ) + ( 23 + 24 ) + ... + ( 22009 + 22010 )
= 21( 1 + 2 ) + 23( 1 + 2 ) + ... + 22009( 1 + 2 )
= 21 . 3 + 23 . 3 + ... + 22009 . 3
= 3( 21 + 23 + ... + 22009 ) ⋮ 3 vì 3 ⋮ 3
Vậy A ⋮ 3
32-5x[3x(4-1)-8]
= 9 - 5 x [ 3 x ( 4 - 1 ) - 8 ]
= 9 - 5 x [ 3 x 3 - 8 ]
= 9 - 5 x [ 9 - 8 ]
= 9 - 5 x 1
= 9 - 5
=4
Ta có: n3+n2+1⋮n+1" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">n3+n2+1⋮n+1n3+n2+1⋮n+1
⇔n2(n+1)+1⋮n+1" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">⇔n2(n+1)+1⋮n+1⇔n2(n+1)+1⋮n+1
mà n2⋅(n+1)⋮n+1" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">n2⋅(n+1)⋮n+1n2⋅(n+1)⋮n+1
nên 1⋮n+1" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">1⋮n+11⋮n+1
⇔n+1∈Ư(1)" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">⇔n+1∈Ư(1)⇔n+1∈Ư(1)
⇔n+1∈{1;−1}" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">⇔n+1∈{1;−1}⇔n+1∈{1;−1}
hay n∈{0;−2}" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">n∈{0;−2}n∈{0;−2}
Vậy: Để n3+n2+1⋮n+1" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">n3+n2+1⋮n+1n3+n2+1⋮n+1 thì n∈{0;−2}" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">n∈{0;−2}
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