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Summer Clouds moderators

08/08/2017 at 08:50
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If positive integers p, q and p + q are all prime, what is the least possible value of pq?




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    Lê Quốc Trần Anh Coordinator 08/08/2017 at 09:13

    The number p,q mustn't be 2 odd number or 2 even number. Because 2 was the only even prime number => p = 2. The least odd prime number is 3 => q = 3.

    So their least possible value is: \(2.3=6\)

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    Phan Thanh Tinh Coordinator 08/08/2017 at 09:21

    p,q are prime numbers,so \(p,q\ge2\) and \(p+q\ge4\)

    => p + q is odd => In 2 numbers p,q,there's an even number and an odd number

    Assume that p is even,then p = 2 and q is odd.If q = 3,then p + q = 5 (satisfied)

    So,the minimum values of p, q, pq are 2,3 and : 2.3 = 6 respectively

    Hence,the answer is 6


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