2: a^2-2*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
3: a^2-3*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
6: a^2-5*d^2 == 0 (mod 3) implies a == 0 (mod 3) and d == 0 (mod 3)
7: a^2-7*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
8: a^2-8*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
10: If n is of the form x^2+2y^2, then 5*n is not of the form x^2+2y^2 and vice versa. Numbers of form x^2+2y^2: No prime factors congruent to 5, 7 (mod 8) to an odd power.
12: a^2-12*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
13: a^2-13*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
14: a^2-5*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7)
15: If n is of the form x^2+3y^2, then 5*n is not of the form x^2+3y^2 and vice versa. Numbers of form x^2+3y^2: No prime factors congruent to 2 (mod 3) to an odd power.
17: a^2-17*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
18: a^2-18*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
21: a^2-5*d^2 == 0 (mod 3) implies a == 0 (mod 3) and d == 0 (mod 3)
22: a^2-22*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
23: a^2-23*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
24: a^2-5*d^2 == 0 (mod 3) implies a == 0 (mod 3) and d == 0 (mod 3)
26: a^2-5*d^2 == 0 (mod 13) implies a == 0 (mod 13) and d == 0 (mod 13)
27: a^2-27*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
28: a^2-28*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
30: If n is of the form x^2+6y^2, then 5*n is not of the form x^2+6y^2 and vice versa. Numbers of form x^2+6y^2: Sum of exponents of 2, 3, 5, 11 (mod 24) prime factors is even.
32: a^2-32*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
33: a^2-33*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
34: a^2-5*d^2 == 0 (mod 17) implies a == 0 (mod 17) and d == 0 (mod 17)
35: If n is of the form x^2+7y^2, then 5*n is not of the form x^2+7y^2 and vice versa. Numbers of form x^2+7y^2: No prime factors congruent to 3, 5, 13 (mod 14) to an odd power.
37: a^2-37*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
38: a^2-38*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
39: a^2-5*d^2 == 0 (mod 3) implies a == 0 (mod 3) and d == 0 (mod 3)
40: If n is of the form x^2+8y^2, then 5*n is not of the form x^2+8y^2 and vice versa. Numbers of form x^2+8y^2: No prime factors congruent to 5, 7 (mod 8) to an odd power.
42: a^2-42*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
43: a^2-43*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
46: a^2-5*d^2 == 0 (mod 23) implies a == 0 (mod 23) and d == 0 (mod 23)
47: a^2-47*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
48: a^2-48*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
50: Substituting a = 5*p, c = 5*q reduces the case to n = 2.
51: a^2-5*d^2 == 0 (mod 3) implies a == 0 (mod 3) and d == 0 (mod 3)
52: a^2-52*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
53: a^2-53*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
54: a^2-5*d^2 == 0 (mod 3) implies a == 0 (mod 3) and d == 0 (mod 3)
56: a^2-5*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7)
57: a^2-57*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
58: a^2-58*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
60: If n is of the form x^2+12y^2, then 5*n is not of the form x^2+12y^2 and vice versa. Numbers of form x^2+12y^2: No prime factors congruent to 2, 5, 11 (mod 12) to an odd power.
62: a^2-62*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
63: a^2-63*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
65: If n is of the form x^2+13y^2, then 5*n is not of the form x^2+13y^2 and vice versa. Numbers of form x^2+13y^2: No prime factors congruent to 3, 5, 21, 23, 27, 33, 35, 37, 41, 43, 45, 51 (mod 52) to an odd power.
66: a^2-5*d^2 == 0 (mod 3) implies a == 0 (mod 3) and d == 0 (mod 3)
67: a^2-67*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
68: a^2-68*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
69: a^2-5*d^2 == 0 (mod 3) implies a == 0 (mod 3) and d == 0 (mod 3)
70: If n is of the form x^2+14y^2, then 5*n is not of the form x^2+14y^2 and vice versa. Numbers of form x^2+14y^2: Sum of exponents of 3, 5, 13, 19, 27, 45 (mod 56) prime factors is even.
72: a^2-72*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
73: a^2-73*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
74: a^2-5*d^2 == 0 (mod 37) implies a == 0 (mod 37) and d == 0 (mod 37)
75: Substituting a = 5*p, c = 5*q reduces the case to n = 3.
77: a^2-77*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
78: a^2-78*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
82: a^2-82*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
83: a^2-83*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
84: a^2-5*d^2 == 0 (mod 3) implies a == 0 (mod 3) and d == 0 (mod 3)
85: If n is of the form x^2+17y^2, then 5*n is not of the form x^2+17y^2 and vice versa. Numbers of form x^2+17y^2: No prime factors congruent to 5, 15, 19, 29, 35, 37, 41, 43, 45, 47, 55, 57, 59, 61, 65, 67 (mod 68) to an odd power.
86: a^2-5*d^2 == 0 (mod 43) implies a == 0 (mod 43) and d == 0 (mod 43)
87: a^2-87*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
88: a^2-88*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
90: If n is of the form x^2+18y^2, then 5*n is not of the form x^2+18y^2 and vice versa. Numbers of form x^2+18y^2: No prime factors congruent to 5, 7, 13, 23 (mod 24) to an odd power.
91: a^2-5*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7)
92: a^2-92*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
93: a^2-93*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
94: a^2-5*d^2 == 0 (mod 47) implies a == 0 (mod 47) and d == 0 (mod 47)
96: a^2-5*d^2 == 0 (mod 3) implies a == 0 (mod 3) and d == 0 (mod 3)
97: a^2-97*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)
98: a^2-98*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5)