# Strange FindInstance output

Posted 8 years ago
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 Want to solve eqn a =.; b =.; c =.; e =.; Solve[3 + 4 a + 4 a^2 + 4 b + 4 b^2 + 4 c + 4 c^2 == 3 (1 + 4 e + 4 e^2), {a, b, c, e}, Integers] output gives 2 conditions {{e -> ConditionalExpression[-(1/2) - Sqrt[ 3 + 4 a + 4 a^2 + 4 b + 4 b^2 + 4 c + 4 c^2]/( 2 Sqrt[3]), ((a | b | c | e) \[Element] Integers && a >= 0) || ((a | b | c | e) \[Element] Integers && a <= -1)]}, {e -> ConditionalExpression[-(1/2) + Sqrt[ 3 + 4 a + 4 a^2 + 4 b + 4 b^2 + 4 c + 4 c^2]/( 2 Sqrt[3]), ((a | b | c | e) \[Element] Integers && a >= 0) || ((a | b | c | e) \[Element] Integers && a <= -1)]}} when I consider the case where e is an odd integer a =.; b =.; c =.; e =.; FindInstance[ e == -(1/2) + Sqrt[3 + 4 a + 4 a^2 + 4 b + 4 b^2 + 4 c + 4 c^2]/( 2 Sqrt[3]) && Mod[e, 2] == 1 && a <= -1, {a, b, c, e}, Integers] I get strange output {{a -> {{-2, 0, 0, 0}} + {0, 1, 1, 1}, b -> {{-2, 0, 0, 0}} + {0, 1, 1, 1}, c -> {{-2, 0, 0, 0}} + {0, 1, 1, 1}, e -> {{-2, 0, 0, 0}} + {0, 1, 1, 1}}} What does this mean? How do you interpret the output? Any comments appreciated.