3: a^2-3*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 5: a^2-5*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 6: a^2-6*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 7: If n is of the form x^2+y^2, then 7*n is not of the form x^2+y^2, and vice versa. Numbers of the form x^2+y^2: No prime factors congruent to 3 (mod 4) to an odd power. 10: a^2-10*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 11: a^2-7*d^2 == 0 (mod 11) implies a == 0 (mod 11) and d == 0 (mod 11) 12: a^2-12*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 13: a^2-13*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 14: If n is of the form x^2+2y^2, then 7*n is not of the form x^2+2y^2, and vice versa. Numbers of the form x^2+2y^2: No prime factors congruent to 5, 7 (mod 8) to an odd power. 15: a^2-7*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5) 17: a^2-17*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 19: a^2-19*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 20: a^2-20*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 22: a^2-7*d^2 == 0 (mod 11) implies a == 0 (mod 11) and d == 0 (mod 11) 23: a^2-7*d^2 == 0 (mod 23) implies a == 0 (mod 23) and d == 0 (mod 23) 24: a^2-24*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 26: a^2-26*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 27: a^2-27*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 28: If n is of the form x^2+4y^2, then 7*n is not of the form x^2+4y^2, and vice versa. Numbers of the form x^2+4y^2: No prime factors congruent to 3 (mod 4) to an odd power. 30: a^2-7*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5) 31: a^2-31*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 33: a^2-32*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 34: a^2-34*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 35: If n is of the form x^2+5y^2, then 7*n is not of the form x^2+5y^2, and vice versa. Numbers of the form x^2+5y^2: sum of exponents of 2, 3, 7 (mod 20) prime factors is even. 38: a^2-38*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 39: a^2-7*d^2 == 0 (mod 13) implies a == 0 (mod 13) and d == 0 (mod 13) 40: a^2-40*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 41: a^2-41*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 43: a^2-7*d^2 == 0 (mod 43) implies a == 0 (mod 43) and d == 0 (mod 43) 44: a^2-7*d^2 == 0 (mod 11) implies a == 0 (mod 11) and d == 0 (mod 11) 45: a^2-45*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 46: a^2-7*d^2 == 0 (mod 23) implies a == 0 (mod 23) and d == 0 (mod 23) 47: a^2-47*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 48: a^2-48*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 51: a^2-7*d^2 == 0 (mod 17) implies a == 0 (mod 17) and d == 0 (mod 17) 52: a^2-52*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 54: a^2-54*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 55: a^2-55*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 56: If n is of the form x^2+8y^2, then 7*n is not of the form x^2+8y^2, and vice versa. Numbers of the form x^2+8y^2: No prime factors congruent to 5, 7 (mod 8) to an odd power. 59: a^2-59*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 60: a^2-7*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5) 61: a^2-61*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 62: a^2-62*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 63: If n is of the form x^2+9y^2, then 7*n is not of the form x^2+9y^2, and vice versa. Numbers of the form x^2+9y^2: No prime factors congruent to 3 (mod 4) to an odd power. 65: a^2-7*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5) 66: a^2-66*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 67: a^2-7*d^2 == 0 (mod 67) implies a == 0 (mod 67) and d == 0 (mod 67) 68: a^2-68*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 69: a^2-69*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 70: If n is of the form x^2+10y^2, then 7*n is not of the form x^2+10y^2, and vice versa. Numbers of the form x^2+10y^2: sum of exponents of 2, 5, 7, 13, 23, 37 (mod 40) prime factors is even. 71: a^2-7*d^2 == 0 (mod 71) implies a == 0 (mod 71) and d == 0 (mod 71) 73: a^2-73*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 75: a^2-75*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 76: a^2-76*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 77: If n is of the form x^2+11y^2, then 7*n is not of the form x^2+11y^2, and vice versa. Numbers of the form x^2+11y^2: No prime factors congruent to 2, 6, 7, 8, 10 (mod 11) to an odd power. 78: a^2-7*d^2 == 0 (mod 13) implies a == 0 (mod 13) and d == 0 (mod 13) 79: a^2-7*d^2 == 0 (mod 79) implies a == 0 (mod 79) and d == 0 (mod 79) 80: a^2-80*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 82: a^2-82*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 83: a^2-83*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 85: a^2-7*d^2 == 0 (mod 17) implies a == 0 (mod 17) and d == 0 (mod 17) 86: a^2-7*d^2 == 0 (mod 43) implies a == 0 (mod 43) and d == 0 (mod 43) 87: a^2-87*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 88: a^2-7*d^2 == 0 (mod 11) implies a == 0 (mod 11) and d == 0 (mod 11) 89: a^2-89*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 90: a^2-90*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 91: If n is of the form x^2+13y^2, then 7*n is not of the form x^2+13y^2, and vice versa. Numbers of the form x^2+13y^2: sum of exponents of 2, 7, 11, 15, 19, 31, 47 mod 52 prime factors is even. 92: a^2-7*d^2 == 0 (mod 23) implies a == 0 (mod 23) and d == 0 (mod 23) 94: a^2-94*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 95: a^2-7*d^2 == 0 (mod 5) implies a == 0 (mod 5) and d == 0 (mod 5) 96: a^2-96*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 97: a^2-97*d^2 == 0 (mod 7) implies a == 0 (mod 7) and d == 0 (mod 7) 99: a^2-7*d^2 == 0 (mod 11) implies a == 0 (mod 11) and d == 0 (mod 11)