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prove this.......on divisibility ?
prove that 13^(2n + 1) + 9^(2n + 1) is divisible by 22 by the process of divisibility ???
2 Answers
- dennisLv 69 years agoFavorite Answer
13^(2n+1) is an odd number , and 9^(2n +1) is also odd so there sum is even
so we only need to prove that 13^(2n + 1) + 9^(2n + 1) is divisible by 11
Now 13 = 2 (mod 11) and 9 = - 2 (mod 11)
So 13^(2n + 1) + 9^(2n + 1) = 2^(2n +1) + (- 2)^(2n+1) = 0(mod 11), hence the result.
- 9 years ago
a^n +b^n = (a+b)( a^(n-1) - a^(n-2) b +a^(n-3) b^2 -............................+b^(n-1)
n is odd
Source(s): www.jeemath.blogspot.in
