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

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

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.