Show that if N is an integer greater than zero, either it is a perfect square, or is not a rational number.
Any integer greater than 1, which is not a power of 2, can be written as the sum of two or more consecutive integers.
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.