Is extern "C" only required on the function declaration?

Edit:
Seems like I had misunderstood the question. Anyways, I tried:

// foo.cpp
/* Function definition */

#include "foo.h"

void foo(int i) {
 //do stuff
}
void test(int i)
{
// do stuff
}

// foo.h
#ifdef __cplusplus
extern "C" {
#endif

/* Function declaration */
void foo(int);

#ifdef __cplusplus
}
#endif

void test(int);

Using command nm to view the symbols from the compiled file:

linuxuser$ nm foo.o
00000006 T _Z4testi
         U __gxx_personality_v0
00000000 T foo

This clearly suggests that the name of function declared as extern "C" is not mangled and the extern "C" keyword is not required at definition.
Had it required every C library code written without extern "C" would have been unusable in C++ programs.

The 'extern "C"' should not be required on the function defintion as long as the declaration has it and is already seen in the compilation of the definition. The standard specifically states (7.5/5 Linkage specifications):

A function can be declared without a linkage specification after an explicit linkage specification has been seen; the linkage explicitly specified in the earlier declaration is not affected by such a function declaration.

However, I generally do put the 'extern "C"' on the definition as well, because it is in fact a function with extern "C" linkage. A lot of people hate when unnecessary, redundant stuff is on declarations (like putting virtual on method overrides), but I'm not one of them.