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

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

Consider the following statements. For any integer n, I. n^(2)+3 is never divisible by 17. II. n^(2)+4 is never divisible by 17. Then

Consider the following statements: 1. a^n+b^n is divisible by a+b if n=2k+1, where k is a positive integer. 2. a^n-b^n is divisible by a-b if n=2k , where k is a positive integer. Which of the statements given above is /are correct? (a) 1 only (b) 2 only (c) both 1 and 2 (d) Neither 1 nor 2

Show that the following statement is true: The integer n is even if and only if n^2 is even

(x^(n)-a^(n)) is divisible by (x-a) for all values of n (b) only for even values of n (c) only for odd values of n(d) only for prime values of n

Show that the following statement is true: The integer n is even if and only if n^(2) is even

Show that 2^(2n) + 1 or 2^(2n)-1 is divisible by 5 according as n is odd or even.

For an integer n, a student states the following : I. If n is odd, (n+1)^(2) is even . II. If n is even (n-1)^(2) is odd. III. If n is even sqrt((n-1)) is irrational . Which of the above statements would be true ?

n(n^(2)-1), is divisible by 24 if n is an odd positive number.

The value of i^(1+3+5+...+(2n+1)) is (1) if n is even,-i if n is odd (2)1 if n is even -1 if n is odd (3)1 if n is odd -1 if n is even (4) none of these