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