Pythagorean Triangles

Please help me with the following problem:

a) 3^2 + 4^2 = 5^2
   20^2 + 21^2 = 29^2
   119^2 + 120^2 = 169^2
  
   To find another such relation, show that if a^2 + (a+1)^2 = c^2, then
(3a+2c+1)^2 + (3a+2c+2)^2 = (4a+3c+2)^2.

(b) If a^2 + (a+1)^2 = c^2, let u=c-a-1 and v=(2a+1-c)/2.  Show that v is an integer and that u(u+1)/2 = v^2.  This shows that there are infinitely many square triangular numbers.

Please show as much detail as possible.  Thanks in advance for the help.