what's the output of:

dpkg --print-architecture

As discussed in the trisquel forum the i3, i5 and i7 processors should be taken as a amd64 or x86-64 and maybe renaming the architectures on the submit form would be a better to avoid thinking on Intel or AMD as a processor platform instead of the real x86/x86-64 processors.

According to the info that Michał Masłowski gave us on the mailing list then we could set something like:

Open a terminal and type the following command:

cat /proc/cpuinfo | grep "lm"

If you get a message like this:

flags		: fpu vme de pse tsc msr pae mce cx8 apic mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe nx lm constant_tsc arch_perfmon pebs bts aperfmperf pni dtes64 monitor ds_cpl est tm2 ssse3 cx16 xtpr pdcm lahf_lm

then you machine is x86-64/amd64 capable and you could choose a x86-64/amd64 distro to run on it