Definition:Salem Constant

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The Salem constant is the greatest real root of Lehmer's polynomial:

$x^{10} + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1 = 0$

Its value is approximately:

$1 \cdotp 17628 \, 08182 \, 599 \ldots$

This sequence is A073011 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also known as

The Salem constant is also known as Lehmer's constant, for Derrick Henry Lehmer, but there is already a constant with that name.

Source of Name

This entry was named for Raphaël Salem.

Historical Note

The Salem constant was discovered by Derrick Henry Lehmer in $1933$.

It was conjectured in $1977$ by David William Boyd that it is the smallest of the Salem numbers.