## Each of A+B+C+D and A^2+B^2+C^2+D^2 is a square — Part 1

$A \; + B \; + \; C \; + \; D \; = \; N^2$

$A^2 \; + \; B^2 \; + \; C^2 \; + \; D^2 \; = \; M^2$

with   $N \; \leq \; 100$

when   A = 1

In my next blog,   $1 < A \leq 9$

$1+4+8+12 = 5^2$ ………. $1^2+4^2+8^2+12^2 = 15^2$
$1+5+13+17 = 6^2$ ……… $1^2+5^2+13^2+17^2 = 22^2$
$1+2+14+32 = 7^2$ ……… $1^2+2^2+14^2+32^2 = 35^2$
$1+10+30+40 = 9^2$ …….. $1^2+10^2+30^2+40^2 = 51^2$

$1+2+30+88 = 11^2$ …….. $1^2+2^2+30^2+88^2 = 93^2$
$1+7+25+111 = 12^2$ ……. $1^2+7^2+25^2+111^2 = 114^2$
$1+6+16+146 = 13^2$ ……. $1^2+6^2+16^2+146^2 = 147^2$
$1+5+73+117 = 14^2$ ……. $1^2+5^2+73^2+117^2 = 138^2$
$1+2+20+202 = 15^2$ ……. $1^2+2^2+20^2+202^2 = 203^2$
$1+3+65+187 = 16^2$ ……. $1^2+3^2+65^2+187^2 = 198^2$
$1+2+80+206 = 17^2$ ……. $1^2+2^2+80^2+206^2 = 221^2$
$1+5+125+193 = 18^2$ …… $1^2+5^2+125^2+193^2 = 230^2$
$1+8+78+274 = 19^2$ ……. $1^2+8^2+78^2+274^2 = 285^2$

$1+3+27+369 = 20^2$ ……. $1^2+3^2+27^2+369^2 = 370^2$
$1+8+142+290 = 21^2$ …… $1^2+8^2+142^2+290^2 = 323^2$
$1+17+121+345 = 22^2$ ….. $1^2+17^2+121^2+345^2 = 366^2$
$1+10+52+466 = 23^2$ …… $1^2+10^2+52^2+466^2 = 469^2$
$1+7+273+295 = 24^2$ …… $1^2+7^2+273^2+295^2 = 402^2$
$1+2+200+422 = 25^2$ …… $1^2+2^2+200^2+422^2 = 467^2$
$1+5+77+593 = 26^2$ ……. $1^2+5^2+77^2+593^2 = 598^2$
$1+2+106+620 = 27^2$ …… $1^2+2^2+106^2+620^2 = 629^2$
$1+7+65+711 = 28^2$ ……. $1^2+7^2+65^2+711^2 = 714^2$
$1+2+68+770 = 29^2$ ……. $1^2+2^2+68^2+770^2 = 773^2$

$1+5+41+853 = 30^2$ ……. $1^2+5^2+41^2+853^2 = 854^2$
$1+8+328+624 = 31^2$ …… $1^2+8^2+328^2+624^2 = 705^2$
$1+11+187+825 = 32^2$ ….. $1^2+11^2+187^2+825^2 = 846^2$
$1+10+256+822 = 33^2$ ….. $1^2+10^2+256^2+822^2 = 861^2$
$1+13+45+1097 = 34^2$ ….. $1^2+13^2+45^2+1097^2 = 1098^2$
$1+4+124+1096 = 35^2$ ….. $1^2+4^2+124^2+1096^2 = 1103^2$
$1+3+355+937 = 36^2$ …… $1^2+3^2+355^2+937^2 = 1002^2$
$1+2+376+990 = 37^2$ …… $1^2+2^2+376^2+990^2 = 1059^2$
$1+5+377+1061 = 38^2$ ….. $1^2+5^2+377^2+1061^2 = 1126^2$
$1+8+92+1420 = 39^2$ …… $1^2+8^2+92^2+1420^2 = 1423^2$

$1+3+177+1419 = 40^2$ ….. $1^2+3^2+177^2+1419^2 = 1430^2$
$1+2+422+1256 = 41^2$ ….. $1^2+2^2+422^2+1256^2 = 1325^2$
$1+25+557+1181 = 42^2$ …. $1^2+25^2+557^2+1181^2 = 1306^2$
$1+18+400+1430 = 43^2$ …. $1^2+18^2+400^2+1430^2 = 1485^2$
$1+17+103+1815 = 44^2$ …. $1^2+17^2+103^2+1815^2 = 1818^2$
$1+2+394+1628 = 45^2$ ….. $1^2+2^2+394^2+1628^2 = 1675^2$
$1+5+577+1533 = 46^2$ ….. $1^2+5^2+577^2+1533^2 = 1638^2$
$1+4+112+2092 = 47^2$ ….. $1^2+4^2+112^2+2092^2 = 2095^2$
$1+7+359+1937 = 48^2$ ….. $1^2+7^2+359^2+1937^2 = 1970^2$
$1+2+150+2248 = 49^2$ ….. $1^2+2^2+150^2+2248^2 = 2253^2$

$1+5+153+2341 = 50^2$ ….. $1^2+5^2+153^2+2341^2 = 2346^2$
$1+8+404+2188 = 51^2$ ….. $1^2+8^2+404^2+2188^2 = 2225^2$
$1+15+343+2345 = 52^2$ …. $1^2+15^2+343^2+2345^2 = 2370^2$
$1+6+522+2280 = 53^2$ ….. $1^2+6^2+522^2+2280^2 = 2339^2$
$1+13+165+2737 = 54^2$ …. $1^2+13^2+165^2+2737^2 = 2742^2$
$1+2+628+2394 = 55^2$ ….. $1^2+2^2+628^2+2394^2 = 2475^2$
$1+15+1207+1913 = 56^2$$1^2+15^2+1207^2+1913^2 = 2262^2$
$1+12+256+2980 = 57^2$ …. $1^2+12^2+256^2+2980^2 = 2991^2$
$1+17+1349+1997 = 58^2$$1^2+17^2+1349^2+1997^2 = 2410^2$
$1+2+422+3056 = 59^2$ ….. $1^2+2^2+422^2+3056^2 = 3085^2$

$1+3+385+3211 = 60^2$ ….. $1^2+3^2+385^2+3211^2 = 3234^2$
$1+2+250+3468 = 61^2$ ….. $1^2+2^2+250^2+3468^2 = 3477^2$
$1+5+345+3493 = 62^2$ ….. $1^2+5^2+345^2+3493^2 = 3510^2$
$1+10+866+3092 = 63^2$ …. $1^2+10^2+866^2+3092^2 = 3211^2$
$1+7+553+3535 = 64^2$ ….. $1^2+7^2+553^2+3535^2 = 3578^2$
$1+2+452+3770 = 65^2$ ….. $1^2+2^2+452^2+3770^2 = 3797^2$
$1+13+2017+2325 = 66^2$$1^2+13^2+2017^2+2325^2 = 3078^2$
$1+10+352+4126 = 67^2$ …. $1^2+10^2+352^2+4126^2 = 4141^2$
$1+7+1055+3561 = 68^2$ …. $1^2+7^2+1055^2+3561^2 = 3714^2$
$1+2+166+4592 = 69^2$ ….. $1^2+2^2+166^2+4592^2 = 4595^2$

$1+5+1761+3133 = 70^2$ …. $1^2+5^2+1761^2+3133^2 = 3594^2$
$1+10+292+4738 = 71^2$ …. $1^2+10^2+292^2+4738^2 = 4747^2$
$1+11+425+4747 = 72^2$ …. $1^2+11^2+425^2+4747^2 = 4766^2$
$1+6+102+5220 = 73^2$ ….. $1^2+6^2+102^2+5220^2 = 5221^2$
$1+5+305+5165 = 74^2$ ….. $1^2+5^2+305^2+5165^2 = 5174^2$
$1+4+974+4646 = 75^2$ ….. $1^2+4^2+974^2+4646^2 = 4747^2$
$1+15+345+5415 = 76^2$ …. $1^2+15^2+345^2+5415^2 = 5426^2$
$1+2+1410+4516 = 77^2$ …. $1^2+2^2+1410^2+4516^2 = 4731^2$
$1+21+565+5497 = 78^2$ …. $1^2+21^2+565^2+5497^2 = 5526^2$
$1+8+1184+5048 = 79^2$ …. $1^2+8^2+1184^2+5048^2 = 5185^2$

$1+3+3075+3321 = 80^2$ …. $1^2+3^2+3075^2+3321^2 = 4526^2$
$1+2+1892+4666 = 81^2$ …. $1^2+2^2+1892^2+4666^2 = 5035^2$
$1+5+1297+5421 = 82^2$ …. $1^2+5^2+1297^2+5421^2 = 5574^2$
$1+2+440+6446 = 83^2$ ….. $1^2+2^2+440^2+6446^2 = 6461^2$
$1+3+1363+5689 = 84^2$ …. $1^2+3^2+1363^2+5689^2 = 5850^2$
$1+2+1940+5282 = 85^2$ …. $1^2+2^2+1940^2+5282^2 = 5627^2$
$1+5+773+6617 = 86^2$ ….. $1^2+5^2+773^2+6617^2 = 6662^2$
$1+2+122+7444 = 87^2$ ….. $1^2+2^2+122^2+7444^2 = 7445^2$
$1+11+2081+5651 = 88^2$$1^2+11^2+2081^2+5651^2 = 6022^2$
$1+2+628+7290 = 89^2$ ….. $1^2+2^2+628^2+7290^2 = 7317^2$

$1+5+1141+6953 = 90^2$ …. $1^2+5^2+1141^2+6953^2 = 7046^2$
$1+2+1600+6678 = 91^2$ …. $1^2+2^2+1600^2+6678^2 = 6867^2$
$1+7+3001+5455 = 92^2$ …. $1^2+7^2+3001^2+5455^2 = 6226^2$
$1+2+4232+4414 = 93^2$ …. $1^2+2^2+4232^2+4414^2 = 6115^2$
$1+5+3205+5625 = 94^2$ …. $1^2+5^2+3205^2+5625^2 = 6474^2$
$1+6+718+8300 = 95^2$ ….. $1^2+6^2+718^2+8300^2 = 8331^2$
$1+3+2467+6745 = 96^2$ …. $1^2+3^2+2467^2+6745^2 = 7182^2$
$1+6+136+9266 = 97^2$ ….. $1^2+6^2+136^2+9266^2 = 9267^2$
$1+9+2297+7297 = 98^2$ …. $1^2+9^2+2297^2+7297^2 = 7650^2$
$1+4+1828+7968 = 99^2$ …. $1^2+4^2+1828^2+7968^2 = 8175^2$

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