Using binomial theorem. Prove that `6^n`-5n always leaves remainder 1 when divided by 25.

Using binomial theorem, evaluate (99)^5

Using binomial theorem, compute (98)^5 .

Let a!=0 and p(x) be a polynomial of degree greater than 2. If p(x) leaves reminders a and -a when divided respectively, by x+a and x-a , then the remainder when p(x) is divided by x^2-a^2 is

6^(n)-5 n when divided by 25 leaves the remainder

Expand using Binomial Theorem (x-2y)^(6)

Find the remainder when x^(3) -ax^2+6x-a is divided by x -a.

Find the remainder when the square of any prime number greater than 3 is divided by 6.