**Problem 1:**

Show that if N is an integer greater than zero, either it is a perfect square, or is not a rational number.

**Problem 2:**

Any integer greater than 1, which is not a power of 2, can be written as the sum of two or more consecutive integers.

**Problem 3:**

If p is any prime, and , prove by induction on n, prove that if , then .

*Please present detailed perfect proofs ! The motivation behind such questions is also to understand rigour of mathematics.*

Nalin Pithwa

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