4^n+15n-1 is divißible bit 9
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P(n):4n
+15n−1 is a multiple of 9 for any natural number n.
4n
can be written as (1+3)n
whose binomial expansion gives :
1+3n+9(n C2 )+........+3n+15n−1
which reduces to :
18n+9(n C2 )+........+3n
=9k where k is an integer.
Therefore,
4n +15n−1 is divisible by 9.
Hope it helps.
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