Concatenations: (A,B,C) squares and primes — Part 2

 
 

Find triples   (A, \; B, \; C)   such that

A   is a perfect square.
B   and   C   are prime numbers,   and

A \; || \; B   and   A \; || \; C   are prime numbers and
B \; || \; A   and   C \; || \; A   are perfect squares

 

For example,
 

3481956 \; = \; 1866^2   is a perfect square.
9649   is a prime number.
624067   is a prime number.

3481956 \; || \; 9649 \; = \; 34819569649   is a prime number.
3481956 \; || \; 624067 \; = \; 3481956624067   is a prime number.

9649 \; || \; 3481956 \; = \; 96493481956 \; = \; 310634^2   is a perfect square.
624067 \; || \; 3481956 \; = \; 6240673481956 \; = \; 2498134^2   is a perfect square.

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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