Question

The number of positive integral solutions of the equation x² – y² = 3906 is

• A. More than one
• B. Only one
• C. Zero
• D. None of these

Answer 1

Answer: (C)

Zero

Answer 2

Since x² – y² is even, therefore, either both x and y are even or both x and y are odd. In either case both x+y and x-y are even.

So, 2 divides x +y and also 2 divides x – y

⇒ 2 x 2 divides (x+y) (x – y)

⇒ 4 divides x² – y².

But 4 does not divide 3906. Hence, the given equation has no solution of the said type.