1. For a particle, the de Broglie wavelength is $\lambda = \frac{h}{mv}$ where $h$ is Planck’s constant, $m$ is mass, and $v$ is velocity.

2. Let the electron have mass $m_e$ and velocity $v_e$, and the neutron have mass $m_n$ and velocity $v_n$.

   Their wavelengths are equal, so $\frac{h}{m_e v_e} = \frac{h}{m_n v_n}$ Cancelling $h$: $m_e v_e = m_n v_n$

3. We are told that the velocity of the electron is $x$ times the velocity of neutron: $v_e = x v_n$ Substitute into the wavelength condition: $m_e (x v_n) = m_n v_n$ Cancelling $v_n$: $m_e x = m_n$ So, $x = \frac{m_n}{m_e}$

4. Substitute the given masses: $x = \frac{1.6 \times 10^{-27}}{9.1 \times 10^{-31}}$ $x = \frac{1.6}{9.1} \times 10^{4}$ $x \approx 0.17582 \times 10^{4}$ $x \approx 1758.24$

5. Nearest integer: $x = 1758$

Therefore, the required value is 1758.