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 a positive integer,show that 4^(n)-3n-1 is divisible by 9

If n is a positive integer, show that: 4^n-3n-1 is divisible by 9

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

If n is a positive integer, then 2.4^(2n + 1) + 3^(3n+1) is divisible by :

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. If n is a prime number greater than 5, then n^(4) - 1 is divisible by 2400. 2. Every square number is of the form 5n or (5n - 1) or (5n + 1) where n is a whole number. Which of the above statements is/are correct ?

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