Prove that 11n+2 + 122n+1 is divisible by 133
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Answer:
First, prove it for the base case ofn=1:
11
(1+2)
+12
(2+1)
= 11
3
+12
3
= 1331+1728
= 133(10)+1+1728
=133(10)+1729
=133(10)+133(13)
=133(26)
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