A^n + B^n + C^n + D^n is a square for n=1,2 — (Part 2)

 

Part 1 :   https://benvitalenum3ers.wordpress.com/2015/07/27/an-bn-cn-dn-is-a-square-for-n12/

A \; + \; B \; + \; C \; + \; D \; = \; N^2,
N \; = \; 5, \; 6,  \; \dotsm \; , \; 100
A^2 \; + \; B^2 \; + \; C^2 \; + \; D^2 \; = \; M^2

 
Part 2 :     N \; = \; 100, \; 101, \; 102,  \; \dotsm \; , \; 200
 
Here are the first few:

1 + 3 + 4051 + 5945 = 100^2
1^2 + 3^2 + 4051^2 + 5945^2 = 7194^2

1 + 4 + 3078 + 7118 = 101^2
1^2 + 4^2 + 3078^2 + 7118^2 = 7755^2

1 + 17 + 3281 + 7105 = 102^2
1^2 + 17^2 + 3281^2 + 7105^2 = 7826^2

1 + 2 + 2840 + 7766 = 103^2
1^2 + 2^2 + 2840^2 + 7766^2 = 8269^2

1 + 3 + 859 + 9953 = 104^2
1^2 + 3^2 + 859^2 + 9953^2 = 9990^2

1 + 8 + 254 + 10762 = 105^2
1^2 + 8^2 + 254^2 + 10762^2 = 10765^2

1 + 5 + 3133 + 8097 = 106^2
1^2 + 5^2 + 3133^2 + 8097^2 = 8682^2

1 + 2 + 1564 + 9882 = 107^2
1^2 + 2^2 + 1564^2 + 9882^2 = 10005^2

1 + 17 + 1799 + 9847 = 108^2
1^2 + 17^2 + 1799^2 + 9847^2 = 10010^2

1 + 8 + 1520 + 10352 = 109^2
1^2 + 8^2 + 1520^2 + 10352^2 = 10463^2

1 + 13 + 4589 + 7497 = 110^2
1^2 + 13^2 + 4589^2 + 7497^2 = 8790^2

1 + 2 + 1186 + 11132 = 111^2
1^2 + 2^2 + 1186^2 + 11132^2 = 11195^2

1 + 7 + 5415 + 7121 = 112^2
1^2 + 7^2 + 5415^2 + 7121^2 =  8946^2

1 + 10 + 936 + 11822 = 113^2
1^2 + 10^2 + 936^2 + 11822^2 = 11859^2

1 + 17 + 4813 + 8165 = 114^2
1^2 + 17^2 + 4813^2 + 8165^2 = 9478^2

 

Complete the rest.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

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

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