Question
Wed May 23, 2012 By: Rajarshi Basu

If least prime factor of a is 3 and least prime factor of b is 7, find the least prime factor of (a+b.

Expert Reply
Wed May 23, 2012
Since 7 + 3 = 10. The least prime factor of a+b has to be 2; unless a+b is a prime number greater than 2.

Suppose a+b is a prime number greater than 2. Then a+b must be an odd number. So one of a or b must be an even number. Suppose then that a is even. Then the least prime factor of a is 2; which is not 3 or 7. So a cannot be an even number. Nor can b be an even number. Hence a+b can not be a prime number greater than 2 if the least prime factor of a is 3 and b is 7.

Hence the answer is 2.
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