An elementary inequality about the Mahler measure

Let p(z) be a degree n polynomial with zeros z_j, j = 1, 2, …, n. The total distance from the zeros of p to the unit circle is defined as td(p) =^∑n ∣ j =1_{|z j} | −1^∣_. We show that up to scalar multiples, td(p) sits between M(p) −1 and m(p). This leads to an equivalent statement of Lehmer’s problem in terms of td(p). The proof is elementary.