1) How many pairs of positive integers (x,y) satisfy the equation \(x^2-y^2=14\)?
2)The value of the expression
\( (3^{1001}+4^{1002})^2-(3^{1001}-4^{1002})^2\)
is \(k\cdot12^{1001}\) for some positive integer k. What is k?
#2: (31001 + 41002)2 - (31001 - 41002)2
has the form: (a + b)2 - (a - b)2 = (a2 + 2ab + b2) - (a2 - 2ab + b2) = 4ab
For this problem: a = 31001 and b = 41002
---> 4ab = 4·31001·41002 = 4·31001·4·1001 = 16·31001·41001 = 16·(3·4)1001
= 16·121001
+367 
