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2024-06-14 07:36:36
Nếu chia hết cho thì với .
=> Xét thì suy ra chia hết cho .
=> Xét thì .
Suy ra chia hết cho .
Vậy với mọi số tự nhiên , nếu chia hết cho thì chia hết cho .
2024-06-14 07:35:37
Nếu n lẻ thì n3 lẻ
n lẻ <=> n =2k +1 (k ∈ Z)
n^3 =(2k +1)3 =8k3 +3.4k2 +3.2k +1=2( 4k3 +6k2 +3 k) +1
2( 4k3 +6k2 +3 k) chia hết cho 2 => là số chẵn
=>2( 4k3 +6k2 +3 k) +1 là số lẻ => n3 lẻ