Maths puzzle

P + Q = 99, where P and Q are both prime numbers.
(a) Find P and Q. (b) Why are you sure that your answer is the only
correct one?

SOLUTION.

(a) The numbers are 2 and 97.
(b) odd + odd = even.
Even + even = even.
Odd + even = odd.
Since 99 is an odd number, one of the numbers P and Q must be even. 2
is the only even prime number, so one of the numbers is 2. Therefore,
the other number is 99 - 2 = 97.
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