For which one of the following statements can the fact that $12 ^ { 2 } + 16 ^ { 2 } = 20 ^ { 2 }$ be used to produce a counterexample? A If $a , b$ and $c$ are positive integers which satisfy the equation $a ^ { 2 } + b ^ { 2 } = c ^ { 2 }$, and the three numbers have no common divisor, then two of them are odd and the other is even. B The equation $a ^ { 4 } + b ^ { 2 } = c ^ { 2 }$ has no solutions for which $a , b$ and $c$ are positive integers. C The equation $a ^ { 4 } + b ^ { 4 } = c ^ { 4 }$ has no solutions for which $a , b$ and $c$ are positive integers. D If $a , b$ and $c$ are positive integers which satisfy the equation $a ^ { 2 } + b ^ { 2 } = c ^ { 2 }$, then one is the arithmetic mean of the other two.
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For which one of the following statements can the fact that $12 ^ { 2 } + 16 ^ { 2 } = 20 ^ { 2 }$ be used to produce a counterexample?
A If $a , b$ and $c$ are positive integers which satisfy the equation $a ^ { 2 } + b ^ { 2 } = c ^ { 2 }$, and the three numbers have no common divisor, then two of them are odd and the other is even.
B The equation $a ^ { 4 } + b ^ { 2 } = c ^ { 2 }$ has no solutions for which $a , b$ and $c$ are positive integers.
C The equation $a ^ { 4 } + b ^ { 4 } = c ^ { 4 }$ has no solutions for which $a , b$ and $c$ are positive integers.
D If $a , b$ and $c$ are positive integers which satisfy the equation $a ^ { 2 } + b ^ { 2 } = c ^ { 2 }$, then one is the arithmetic mean of the other two.