Toán Lớp 8: https://hoidap247.com/cau-hoi/2265269
CMR :
a)$33^{27}$ + $27^{33}$ chia hết cho 36
b)$3^{2n + 1}$ + $2^{n + 2}$ chia hết cho 7
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Toán Lớp 8: https://hoidap247.com/cau-hoi/2265269
CMR :
a)$33^{27}$ + $27^{33}$ chia hết cho 36
b)$3^{2n + 1}$ + $2^{n + 2}$ chia hết cho 7
Comments ( 2 )
Ta có 33^27 + 27^33
= 3^27 . 11^27 + (3^3)^99
= 3^2 . 11.3^25 . 11^26 + 3^99= 99 . 3^25(11^26.3^74)
= [36. 3 . 3^25(11^26.3^74)] chia hết cho 36.
=> 33^37 + 27^33 chia hết cho 36.
Ta có: 32n + 1 = 3 . 9n ≡3 . 2n (mod 7)
=>2n + 2 = 4 . 2n ≡4 . 2n (mod 7)
=> 32n + 1 + 2n + 2 ≡3 . 2n + 4 . 2n ≡7 . 2n ≡0 (mod 7) (ĐPCM)