Office Applications and Entertainment, Magic Squares Attachment 16.2.4 About the Author

Parametric Solutions for Magic Squares of Squares (4 x 4)
Seiji Tomita

Solution #1, S = 50*(k2+337)
 (2k+105)2 (3k+38)2 (6k-59)2 (k+30)2 (k-66)2 (6k+5)2 (3k+70)2 (2k-87)2 (3k-38)2 (2k-105)2 (k-30)2 (6k+59)2 (6k-5)2 (k+66)2 (2k+87)2 (3k-70)2
Solution #2, S = 130*(k2+281)
 (3k+154)2 (6k+13)2 (9k-78)2 (2k+81)2 (2k-111)2 (9k+18)2 (6k+77)2 (3k-134)2 (6k-13)2 (3k-154)2 (2k-81)2 (9k+78)2 (9k-18)2 (2k+111)2 (3k+134)2 (6k-77)2
Solution #3, S = 125*(k2+373)
 (4k+165)2 (6k+2)2 (8k-114)2 (3k+80)2 (3k-136)2 (8k+30)2 (6k+110)2 (4k-123)2 (6k-2)2 (4k-165)2 (3k-80)2 (8k+114)2 (8k-30)2 (3k+136)2 (4k+123)2 (6k-110)2
Solution #4, S = 130*(2k2+53)
 (3k+70)2 (5k+33)2 (15k-26)2 (k+15)2 (k-30)2 (15k+1)2 (5k+42)2 (3k-65)2 (5k-33)2 (3k-70)2 (k-15)2 (15k+26)2 (15k-1)2 (k+30)2 (3k+65)2 (5k-42)2
Solution #5, S = 145*(k2+74)
 (4k+80)2 (5k+36)2 (10k-53)2 (2k+15)2 (2k-55)2 (10k+3)2 (5k+64)2 (4k-60)2 (5k-36)2 (4k-80)2 (2k-15)2 (10k+53)2 (10k-3)2 (2k+55)2 (4k+60)2 (5k-64)2
Solution #6, S = 340*(k2+29)
 (5k+81)2 (9k+15)2 (15k-43)2 (3k+35)2 (3k-55)2 (15k+7)2 (9k+45)2 (5k-69)2 (9k-15)2 (5k-81)2 (3k-35)2 (15k+43)2 (15k-7)2 (3k+55)2 (5k+69)2 (9k-45)2
Solution #7, S = 290*(2k2+37)
 (7k+81)2 (9k+42)2 (21k-47)2 (3k+14)2 (3k-49)2 (21k+2)2 (9k+63)2 (7k-66)2 (9k-42)2 (7k-81)2 (3k-14)2 (21k+47)2 (21k-2)2 (3k+49)2 (7k+66)2 (9k-63)2
Solution #8, S = 130*(k2+281)
 (2k+165)2 (5k+34)2 (10k-57)2 (k+70)2 (k-90)2 (10k+7)2 (5k+66)2 (2k-155)2 (5k-34)2 (2k-165)2 (k-70)2 (10k+57)2 (10k-7)2 (k+90)2 (2k+155)2 (5k-66)2
Solution #9, S = 221*(k2+85)
 (3k+112)2 (8k+6)2 (12k-43)2 (2k+66)2 (2k-78)2 (12k+11)2 (8k+42)2 (3k-104)2 (8k-6)2 (3k-112)2 (2k-66)2 (12k+43)2 (12k-11)2 (2k+78)2 (3k+104)2 (8k-42)2
Solution #10, S = 481*(k2+50)
 (3k+128)2 (12k+4)2 (18k-33)2 (2k+81)2 (2k-87)2 (18k+9)2 (12k+32)2 (3k-124)2 (12k-4)2 (3k-128)2 (2k-81)2 (18k+33)2 (18k-9)2 (2k+87)2 (3k+124)2 (12k-32)2
Solution #11, S = 325*(k2+149)
 (8k+162)2 (9k+24)2 (12k-143)2 (6k+34)2 (6k-146)2 (12k+17)2 (9k+144)2 (8k-78)2 (9k-24)2 (8k-162)2 (6k-34)2 (12k+143)2 (12k-17)2 (6k+146)2 (8k+78)2 (9k-144)2