1. Prove the following statement using the method of contradiction:
There are no positive integer solutions to the Diophantine equation x2 - y2 = 1.
2. Prove the following statement using contraposition: If n, is a positive integer such that n(mod 3) = 2, then n is not a perfect square.
3. Find a solution (if it exists) to the linear diophantine equation 234x + 65y = 325.
4. Prove that the sum to n terms of the sequence
![782_method of contradiction.png](https://secure.tutorsglobe.com/CMSImages/782_method%20of%20contradiction.png)
5. Prove using mathematical induction, that n3 - 7n + 3 is divisible by 3 for each integer n > 0.
6. The terms of a sequence are given recursively as
![396_method of contradiction1.png](https://secure.tutorsglobe.com/CMSImages/396_method%20of%20contradiction1.png)
7. In each case decide whether the statement is true or false.
![1085_method of contradiction2.png](https://secure.tutorsglobe.com/CMSImages/1085_method of contradiction2.png)