Squarefree semiprimes (A,B,C); A+B,B+C,C+A

 
 
Can you find squarefree semiprimes A, B, C such that each of

A + B
B + C
C + A

is a square number?

 
 

Paul found:

14 + 86 \; = \; (2 \times 7) + (2 \times 43) \; = \; 10^2
86 + 35 \; = \; (2 \times 43) + (5 \times 7) \; = 11^2
14 + 35 \; = \; (2 \times 7) + (5 \times 7) \; = \; 7^2

26 + 74 \; = \; (2 \times 13) + (2 \times 37) \; = \; 10^2
74 + 95 \; = \; (2 \times 37) + (5 \times 19) \; = \; 13^2
26 + 95 \; = \; (2 \times 13) + (5 \times 19) \; = \; 11^2

38 + 106 \; = \; (2 \times 19) + (2 \times 53) \; = \; 12^2
106 + 218 \; = \; (2 \times 53) + (2 \times 109) \; = \; 18^2
38 + 218 \; = \; (2 \times 19) + (2 \times 109) \; = \; 16^2

38 + 158 \; = \; (2 \times 19) + (2 \times 79) \; = \; 14^2
158 + 803 \; = \; (2 \times 79) + (11 \times 73) \; = \; 31^2
38 + 803 \; = \; (2 \times 19) + (11 \times 73) \; = \; 29^2

106 + 218 \; = \; (2 \times 53) + (2 \times 109) \; = \; 18^2
218 + 623 \; = \; (2 \times 109) + (7 \times 89) \; = \; 29^2
106 + 623 \; = \; (2 \times 53) + (7 \times 89) \; = \; 27^2

118 + 206 \; = \; (2 \times 59) + (2 \times 103) \; = \; 18^2
206 + 323 \; = \; (2 \times 103) + (17 \times 19) \; = \; 23^2
118 + 323 \; = \; (2 \times 59) + (17 \times 19) \; = \; 21^2

 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

2 Responses to Squarefree semiprimes (A,B,C); A+B,B+C,C+A

  1. paul says:

    Here are a few

    14 + 86 = 10^2
    86 + 35 = 11^2
    14 + 35 = 7^2

    26 + 74 = 10^2
    74 + 95 = 13^2
    26 + 95 = 11^2

    38 + 106 = 12^2
    106 + 218 = 18^2
    38 + 218 = 16^2

    38 + 158 = 14^2
    158 + 803 = 31^2
    38 + 803 = 29^2

    106 + 218 = 18^2
    218 + 623 = 29^2
    106 + 623 = 27^2

    118 + 206 = 18^2
    206 + 323 = 23^2
    118 + 323 = 21^2

    Paul

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