and 
are
two odd prime numbers, show that 
is
composite.
Answer:
a2 - b2 = (a - b) (a + b)
If a and b are odd, then let a = 2k + 1, b = 2n + 1
a - b = (2k + 1) - (2n + 1) = 2 (k - n)
a + b = (2k + 1) + (2n + 1) = 2 (k + n + 1)
neither
of the two divisors (a - b) and (a + b) is equal to 1. a2
- b2 is composite
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