[5.n2-1" is divisible by "8" if "n" is "^(*)],[" integer "],[" natural no."],[" even no."],[" odd no."]

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

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

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

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

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

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

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

If n is an odd integer, prove that n^(2) is also an odd 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

The natural numbers ware not sufficient to deal with various equations that mathematicians encountered so some new sets of numbers were defined Ehole numbers (W) = {0,1,2,3,4,……….} Integers (Z or I) = (……, -3,-2,-1,1,0,2,3,4,……} Even integers :- Intigers divisible by 2, they are expressed as 2n n in Z. odd Integers :- Integers not divisible by 2, they are expressed as 2n+1or 2n-1,ninZ. Difference of squarees of two odd integeers is always divisible by