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Stefan Kohl
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cyclotomic Cyclotomic polynomials with 7$^{th}$ coefficient greater than 1 in absolute value

It'sIt is known that the seventh coefficient of $\Phi_{105}(x)$ is $-2$ and that's the first occurrence of a coefficient with absolute value greater than $1$ for a cyclotomic polynomial. When I did a quick check for the seventh coefficient of $\Phi_n(x)$ where $n=105k$ with $\gcd(105,k)=1$ and $\mu(k)\neq 0$ they all came out to be $2$ in absolute value whenever they are nonzero. Is it true in general or there is a counterexample to this?

cyclotomic polynomials with 7$^{th}$ coefficient greater than 1 in absolute value

It's known that the seventh coefficient of $\Phi_{105}(x)$ is $-2$ and that's the first occurrence of a coefficient with absolute value greater than $1$ for a cyclotomic polynomial. When I did a quick check for the seventh coefficient of $\Phi_n(x)$ where $n=105k$ with $\gcd(105,k)=1$ and $\mu(k)\neq 0$ they all came out to be $2$ in absolute value whenever they are nonzero. Is it true in general or there is a counterexample to this?

Cyclotomic polynomials with 7$^{th}$ coefficient greater than 1 in absolute value

It is known that the seventh coefficient of $\Phi_{105}(x)$ is $-2$ and that's the first occurrence of a coefficient with absolute value greater than $1$ for a cyclotomic polynomial. When I did a quick check for the seventh coefficient of $\Phi_n(x)$ where $n=105k$ with $\gcd(105,k)=1$ and $\mu(k)\neq 0$ they all came out to be $2$ in absolute value whenever they are nonzero. Is it true in general or there is a counterexample to this?

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It's known that the seventh coefficient of $\Phi_{105}(x)$ is $-2$ and that's the first occurrence of a coefficient with absolute value greater than $1$ for a cyclotomic polynomial. When I did a quick check for the seventh coefficient of $\Phi_n(x)$ where $n=105k$ with $\gcd(105,k)=1$ and $\mu(k)\neq 0$ they all came out to be greater than $1$ $2$ in absolute value whenever they are nonzero. Is it true in general or there is a counterexample to this?

It's known that the seventh coefficient of $\Phi_{105}(x)$ is $-2$ and that's the first occurrence of a coefficient with absolute value greater than $1$ for a cyclotomic polynomial. When I did a quick check for the seventh coefficient of $\Phi_n(x)$ where $n=105k$ with $\gcd(105,k)=1$ and $\mu(k)\neq 0$ they all came out to be greater than $1$ in absolute value. Is it true in general or there is a counterexample to this?

It's known that the seventh coefficient of $\Phi_{105}(x)$ is $-2$ and that's the first occurrence of a coefficient with absolute value greater than $1$ for a cyclotomic polynomial. When I did a quick check for the seventh coefficient of $\Phi_n(x)$ where $n=105k$ with $\gcd(105,k)=1$ and $\mu(k)\neq 0$ they all came out to be $2$ in absolute value whenever they are nonzero. Is it true in general or there is a counterexample to this?

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Michael Hardy
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It's known that the seventh coefficient of $\Phi_{105}(x)$ is -2$-2$ and that's the first occurrence of a coefficient with absolute value greater than 1$1$ for a cyclotomic polynomial. When I did a quick check for the seventh coefficient of $\Phi_{n}(x)$$\Phi_n(x)$ where $n=105k$ with gcd$(105,k)=1$$\gcd(105,k)=1$ and $\mu(k)\neq 0$ they all came out to be greater than 1$1$ in absolute value. Is it true in general or there is a counterexample to this?

It's known that the seventh coefficient of $\Phi_{105}(x)$ is -2 and that's the first occurrence of a coefficient with absolute value greater than 1 for a cyclotomic polynomial. When I did a quick check for the seventh coefficient of $\Phi_{n}(x)$ where $n=105k$ with gcd$(105,k)=1$ and $\mu(k)\neq 0$ they all came out to be greater than 1 in absolute value. Is it true in general or there is a counterexample to this?

It's known that the seventh coefficient of $\Phi_{105}(x)$ is $-2$ and that's the first occurrence of a coefficient with absolute value greater than $1$ for a cyclotomic polynomial. When I did a quick check for the seventh coefficient of $\Phi_n(x)$ where $n=105k$ with $\gcd(105,k)=1$ and $\mu(k)\neq 0$ they all came out to be greater than $1$ in absolute value. Is it true in general or there is a counterexample to this?

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