Prove the following concerning triangular numbers:

a) A number is triangular if and only if it is of the form n(n+1)/2 for some n≧1

b) the integer n is a triangular number if and only if 8n+1is a perfect square

c) the sum of any two consecutive triangular numbers is a perfect square

d) if n is a triangular, then so are 9n+1, 25n+3,and 49n+6