Show that: `2^(4n)-2^n(7n+1)` is some multiple of the square of 14, where n is a positive integer.

(-i)^(4n+3) , where n Is a positive integer.

Show that ((-1+sqrt(3)i)/2)^n+((-1-sqrt(3i))/2)^n is equal to 2 when n is a multiple of 3 and is equal to -1 when n is any other positive integer.

Show that 9^(n+1)-8n-9 is divisible by 64, where n is a positive integer.

Show that 9^(n+1)-8n-9 is divisible by 64, where n is a positive integer.

By using binomial theorem prove that (2^(3n)-7n-1) is divisible by 49 where n is a positive integer.

Prove that 2^n > n for all positive integers n.

Show that 7^(n) +5 is divisible by 6, where n is a positive integer

Show that one and only one out of n ,n+2 or n+4 is divisible by 3, where n is any positive integer.

Show that one and only one out of n ,n+2or ,n+4 is divisible by 3, where n is any positive integer.

Prove that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.