Question:
if a and b are two odd prime numbers , show that a square - b square is composite .
Answer:
Given, a and b are two odd prime numbers.
Let us assume that a > b
Since a, b are both are odd numbers
So, a - b ≥ 2
Also, b ≥ 3, a ≥ 5
Now a2 - b2 = (a - b)*(a + b), where a + b > a ≥ 5, and a - b ≥ 2
Since (a - b)and (a + b) are factors of a2 - b2
So, a2 - b2 is a composite number.
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