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if you excute the command sudo update-grub it would update your grub boot list to point to the 3.16.0-35 kernel in the first place, hence it will be the default kernel. what you have is a case where you booted in using 3.13 instead of the "latest on your machine" kernel which is 3.16.0-24
You have to download proper kernel-headers. From what I see in my Ubuntu there is a proper package: linux-headers-3.13.0-35-generic - Linux kernel headers for version 3.13.0 on 32 bit x86 SMP apt-cache search linux-headers should show you what is available apt-get install linux-headers-3.13.0-35-generic should help you getting the proper linux-headers, ...
You are currently running a 3.13 kernel for which support was ended long ago. Try to install the linux-generic package which will pull in a kernel image and headers which matches each other. Then reboot.
I try and install it on Ubuntu 14.04 "Trusty Tahr" trough the method suggested by Wajid and Jos, but it is better to check first the final release into the tcpdump release, then choose what you need, and install it in the way he suggested. Of course replace the release with the wished one.
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