If `(12^n+1)\ ` is divisible by 13, then n is (a) 1 only (b) 12 only (c) any odd integer (d) any even integer

If the number (1-i)^n/(1+i)^(n-2) is real and positive then n is (a) Any Integer (b) Any odd Integer (c) Any even Integer (d) None of these

Let a, b, c be such that b(a""+""c)!=0 . If |a a+1a-1-bb+1b-1cc-1c+1|+|a+1b+1c-1a-1b-1c+1(-1)^(n+2)a(-1)^(n+1)b(-1)^n c|=0 then the value of n is (1) zero (2) any even integer (3) any odd integer (4) any integer

If (9 + sqrt80)^n =1+f, where I, n are integers and 0 lt f lt 0 : (A) I is an odd Integer (B) I is even integer (C) (I+f) (1-f)=1 (D) 1-f=(9-sqrt 80)^n

Consider the following statements: For any positive integer n, the number 10^n-1 is divisible by 9 for n = odd only (2) 9 for n = even only 11 for n = odd only (4) 11 for n = even only Which of the above statements are correct? 1 and 3 (b) 2 and 3 (c) 1 and 4 (d) 2 and 4

Show that a^(n) - b^(n) is divisible by a – b if n is any positive integer odd or even.

If n is an odd integer then n ^(2) -1 is divisible by

Show that a^(n) - b^(n) is divisible by (a + b) when n is an even positive integer. but not if n is odd.

Show that n^(2)-1 is divisible by 8, if n is an odd positive integer.

If (4+sqrt(15))^n=I+f,w h r en is an odd natural number, I is an integer and 0

(x+1) is a factor of x^(n)+1 only if n is an odd integer (b) n is an even integer n is a negative integer (d) n is a positive integer