Please help me with Discrete Math.

Direct Proof

The sum of an odd integer and an even integer is an odd integer.

The product of an even integer and an odd integer is an even integer..

Proof by Contraposition

For integers m and n, if m*n is odd, then both m and n are odd.

Proof by contradiction

If 3n+4 is odd, then n is odd.

Induction Method

7 divides 8ⁿ-1 for all integers n greater than or equal to 1.

2n+1=or<2^n for all integers n>or=3