a)
Ta có: 11n+2 + 122n+1 = 121.11n + 12.144n = 133.11n + 12.(144n – 11n)
Mà (144n – 11n) ⋮ (144 – 11) nên suy ra: (144n – 11n) ⋮ 133
=> 11n+2 + 122n+1 ⋮ 133 (đpcm)
b)5n+2+26.5n+82n+1=5n.25+26.5n+64.8n=5n(25+26)+64.8n=5n.51+64.8n=5n.59−8.5n+64.5n=5n.59+(64n−5n).85n+2+26.5n+82n+1=5n.25+26.5n+64.8n=5n(25+26)+64.8n=5n.51+64.8n=5n.59−8.5n+64.5n=5n.59+(64n−5n).8chia hết cho 59 (vì 64n−5n64n−5n chia hết cho 64−5=5964−5=59 với mọi n).
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