With the help of bionomial expansion, show that `(4^(n)-3n)` is always leaves remainder 1, when divided by 9.

Using binomial theorem, prove that 8^(n)-7n always leaves remainder 1 when divided by 49.

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

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

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

Using binomial theorem, prove that 6^n-5n always leaves he remainder 1 when divided by 25.

Find remainder when 4444^(4444) is divided by 9

By taking three different values of n verify the truth of the following statements: If n is even, then n^3 is also even. if n is odd, then n^3 is also odd. If n leaven remainder 1 when divided by 3, then n^3 also leaves 1 as remainder when divided by 3. If a natural number n is of the form 3p+2\ t h e n\ n^3 also a number of the same type.

Find 'a' if the two polynomials ax^(3)+3x^(2)-9and2x^(3)+4x+a , leaves the same remainder when divided by x + 3.

635, 98, 122 are not perfect squares as they leave remainder 2 when divided by 3.