A test consists of 10 true/false questions. To pass the test a student must answer at least 66 questions correctly. If a studen
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Proof by contadiction.
Let assume there exist such positive integers and
whose sum is a prime number
, that their greatest common divisor is greater than 1.
Since is a prime number and
, then
, but we assumed earlier that
, and there are no two positive integers that sum up to 1.
q.e.d.