It depends. Something compiled for IA-32 (Intel 32-bit) may run on amd64 as Linux on Intel retains backwards compatibility with 32-bit applications (with suitable software installed). Here's your
code compiled on RedHat 7.3 32-bit system (circa 2002, gcc version 2.96) and then the binary copied over to and run on a Centos 7.4 64-bit system (circa 2017):
-bash-4.2$ file code
code: ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.2.5, not stripped
-bash: ./code: /lib/ld-linux.so.2: bad ELF interpreter: No such file or directory
-bash-4.2$ sudo yum -y install glibc.i686
-bash-4.2$ ./code ; echo $?
Ancient RedHat 7.3 to Centos 7.4 (essentially RedHat Enterprise Linux 7.4) is staying in the same "distribution" family, so will likely have better portability than going from some random "Linux from scratch" install from 2002 to some other random Linux distribution in 2018.
Something compiled for amd64 would not run on 32-bit only releases of Linux (old hardware does not know about new hardware). This is also true for new software compiled on modern systems intended to be run on ancient old things, as libraries and even system calls may not be backwards portable, so may require compilation tricks, or obtaining an old compiler and so forth, or possibly instead compiling on the old system. (This is a good reason to keep virtual machines of ancient old things around.)
Architecture does matter; amd64 (or IA-32) is vastly different from ARM or MIPS so the binary from one of those would not be expected to run on another. At the assembly level the
main section of your code on IA-32 compiles via
gcc -S code.c to
which an amd64 system can deal with (on a Linux system--OpenBSD by contrast on amd64 does not support 32-bit binaries; backwards compatibility with old archs does give attackers wiggle room, e.g. CVE-2014-8866 and friends). Meanwhile on a big-endian MIPS system
main instead compiles to:
which an Intel processor will have no idea what to do with, and likewise for the Intel assembly on MIPS.
You could possibly use QEMU or some other emulator to run foreign code (perhaps very, very slowly).
However! Your code is very simple code, so will have fewer portability issues than anything else; programs typically make use of libraries that have changed over time (glibc, openssl, ...); for those one may also need to install older versions of various libraries (RedHat for example typically puts "compat" somewhere in the package name for such)
or possibly worry about ABI changes (Application Binary Interface) for way old things that use glibc, or more recently changes due to C++11 or other C++ releases. One could also compile static (greatly increasing the binary size on disk) to try to avoid library issues, though whether some old binary did this depends on whether the old Linux distribution was compiling most everything dynamic (RedHat: yes) or not. On the other hand, things like
patchelf can rejigger dynamic (ELF, but probably not
a.out format) binaries to use other libraries.
However! Being able to run a program is one thing, and actually doing something useful with it another. Old 32-bit Intel binaries may have security issues if they depend on a version of OpenSSL that has some horrible and not-backported security problem in it, or the program may not be able to negotiate at all with modern web servers (as the modern servers reject the old protocols and ciphers of the old program), or SSH protocol version 1 is no longer supported, or ...