Prime numbers & sums of 3 squares in 2 ways

 
Case #1 :

14 \; + \; 18 \; + \; 19 \; = \; 15 \; + \; 16 \; + \; 20 \; = \; 51
14^2 \; + \; 18^2 \; + \; 19^2 \; = \; 15^2 \; + \; 16^2 \; + \; 20^2 \; = \; 881   is a prime number

( \, \pi (14), \;  \pi (18), \; \pi (19) \, )   ———->   (43, 61, 67)
( \, \pi (15), \;  \pi (16), \; \pi (20) \, )   ———->   (47, 53, 71)
 

43 \; + \; 61 \; + \; 67 \; = \; 47 \; + \; 53 \; + \; 71 \; = \; 171
43^2 \; + \; 61^2 \; + \; 67^2 \; = \; 47^2 \; + \; 53^2 \; + \; 71^2 \; = \; 10059

 
Case #2 :

 
31 + 35 + 36 \; = \; 102   ……………..   32 + 34 + 37 \; = \; 103
31^2 + 35^2 + 36^2 \; = \; 3482   ……….   32^2 + 34^2 + 37^2 \; = \; 3549

( \, \pi (31), \;  \pi (35), \; \pi (36) \, )   ———->   (127, 149, 151)
( \, \pi (32), \;  \pi (34), \; \pi (37) \, )   ———->   (131, 139, 157)
 

127 \; + \; 149 \; + \; 151 \; = \; 131 \; + \; 139 \; + \; 157 \; = \; 427
127^2 \; + \; 149^2 \; + \; 151^2 \; = \; 131^2 \; + \; 139^2 \; + \; 157^2 \; = \; 61131

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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