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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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Solution d1 solution | Comment 1 of 4

All prime numbers  over 3 are 1 or -1  (mod6), therefore none of the binoms  of A+BC structure will be prime if  A*B*C is an odd number.

It is easy to see that one (and not more than one!) of(A,B,C)  MUST BE   2,  so    ABS(A*B*C)  will be 2,   i.e.

The possible remainders when A+B+C is divided by 6 are either 2 or 4

Example:  2,5,7  generate 37,19,17 ;

 2*5*7=70  whereas 70 divided by 6 gives 11 and remainder 4.


  Posted by Ady TZIDON on 2016-10-17 09:03:30
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