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Prime and Six Settlement (Posted on 2016-10-17) Difficulty: 3 of 5
Each of A, B, C, A+B*C, B+C*A and C+A*B is a prime number.

Find the possible remainders when A+B+C is divided by 6.

No Solution Yet Submitted by K Sengupta    
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sum not product | Comment 2 of 4 |
If a=2, bc=-1mod6 if a+bc=prime.  Then b=1 and c=-1mod6 and (a+b+c)=2mod6.
  Posted by xdog on 2016-10-17 09:37:48
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