Notebook

In [1]:

ENV["LINES"] = 1000

Out[1]:

In [2]:

n = 100
[(a, b, isqrt(a^2+b^2)) for a in 3:n for b in a+1:a^2÷2
    if gcd(a, b) == 1 && a^2 + b^2 == isqrt(a^2 + b^2)^2]

Out[2]:

100-element Vector{Tuple{Int64, Int64, Int64}}:
 (3, 4, 5)
 (5, 12, 13)
 (7, 24, 25)
 (8, 15, 17)
 (9, 40, 41)
 (11, 60, 61)
 (12, 35, 37)
 (13, 84, 85)
 (15, 112, 113)
 (16, 63, 65)
 (17, 144, 145)
 (19, 180, 181)
 (20, 21, 29)
 (20, 99, 101)
 (21, 220, 221)
 (23, 264, 265)
 (24, 143, 145)
 (25, 312, 313)
 (27, 364, 365)
 (28, 45, 53)
 (28, 195, 197)
 (29, 420, 421)
 (31, 480, 481)
 (32, 255, 257)
 (33, 56, 65)
 (33, 544, 545)
 (35, 612, 613)
 (36, 77, 85)
 (36, 323, 325)
 (37, 684, 685)
 (39, 80, 89)
 (39, 760, 761)
 (40, 399, 401)
 (41, 840, 841)
 (43, 924, 925)
 (44, 117, 125)
 (44, 483, 485)
 (45, 1012, 1013)
 (47, 1104, 1105)
 (48, 55, 73)
 (48, 575, 577)
 (49, 1200, 1201)
 (51, 140, 149)
 (51, 1300, 1301)
 (52, 165, 173)
 (52, 675, 677)
 (53, 1404, 1405)
 (55, 1512, 1513)
 (56, 783, 785)
 (57, 176, 185)
 (57, 1624, 1625)
 (59, 1740, 1741)
 (60, 91, 109)
 (60, 221, 229)
 (60, 899, 901)
 (61, 1860, 1861)
 (63, 1984, 1985)
 (64, 1023, 1025)
 (65, 72, 97)
 (65, 2112, 2113)
 (67, 2244, 2245)
 (68, 285, 293)
 (68, 1155, 1157)
 (69, 260, 269)
 (69, 2380, 2381)
 (71, 2520, 2521)
 (72, 1295, 1297)
 (73, 2664, 2665)
 (75, 308, 317)
 (75, 2812, 2813)
 (76, 357, 365)
 (76, 1443, 1445)
 (77, 2964, 2965)
 (79, 3120, 3121)
 (80, 1599, 1601)
 (81, 3280, 3281)
 (83, 3444, 3445)
 (84, 187, 205)
 (84, 437, 445)
 (84, 1763, 1765)
 (85, 132, 157)
 (85, 3612, 3613)
 (87, 416, 425)
 (87, 3784, 3785)
 (88, 105, 137)
 (88, 1935, 1937)
 (89, 3960, 3961)
 (91, 4140, 4141)
 (92, 525, 533)
 (92, 2115, 2117)
 (93, 476, 485)
 (93, 4324, 4325)
 (95, 168, 193)
 (95, 4512, 4513)
 (96, 247, 265)
 (96, 2303, 2305)
 (97, 4704, 4705)
 (99, 4900, 4901)
 (100, 621, 629)
 (100, 2499, 2501)

In [3]:

n = 100
[(a, b, isqrt(a^2+b^2)) for a in 3:n for b in a+1:max(n, a^2÷2)
    if gcd(a, b) == 1 && a^2 + b^2 == isqrt(a^2 + b^2)^2 && b != a^2÷2]

Out[3]:

51-element Vector{Tuple{Int64, Int64, Int64}}:
 (8, 15, 17)
 (12, 35, 37)
 (16, 63, 65)
 (20, 21, 29)
 (20, 99, 101)
 (24, 143, 145)
 (28, 45, 53)
 (28, 195, 197)
 (32, 255, 257)
 (33, 56, 65)
 (36, 77, 85)
 (36, 323, 325)
 (39, 80, 89)
 (40, 399, 401)
 (44, 117, 125)
 (44, 483, 485)
 (48, 55, 73)
 (48, 575, 577)
 (51, 140, 149)
 (52, 165, 173)
 (52, 675, 677)
 (56, 783, 785)
 (57, 176, 185)
 (60, 91, 109)
 (60, 221, 229)
 (60, 899, 901)
 (64, 1023, 1025)
 (65, 72, 97)
 (68, 285, 293)
 (68, 1155, 1157)
 (69, 260, 269)
 (72, 1295, 1297)
 (75, 308, 317)
 (76, 357, 365)
 (76, 1443, 1445)
 (80, 1599, 1601)
 (84, 187, 205)
 (84, 437, 445)
 (84, 1763, 1765)
 (85, 132, 157)
 (87, 416, 425)
 (88, 105, 137)
 (88, 1935, 1937)
 (92, 525, 533)
 (92, 2115, 2117)
 (93, 476, 485)
 (95, 168, 193)
 (96, 247, 265)
 (96, 2303, 2305)
 (100, 621, 629)
 (100, 2499, 2501)

In [ ]: