Yes. unsigned, signed, short, long, long long all are simple type specifiers for XXX int.
See 7.1 Specifiers [dcl.spec] in the standard:
3 [ Note: Since signed, unsigned, long, and short by default imply int, a type-name appearing after one of
  those specifiers is treated as the name being (re)declared. [ Example:
void h(unsigned Pc); // void h(unsigned int)
void k(unsigned int Pc); // void k(unsigned int)
—end example ] —end note ]
and 7.1.6.2 Simple type specifiers [dcl.type.simple]
    Table 10 — simple-type-specifiers and the types they specify
    Specifier(s)            | Type
    ------------------------+---------------------------------
    type-name               | the type named
    simple-template-id      | the type as defined in 14.2
    char                    | “char”
    unsigned char           | “unsigned char”
    signed char             | “signed char”
    char16_t                | “char16_t”
    char32_t                | “char32_t”
    bool                    | “bool” 
    unsigned                | “unsigned int”
    unsigned int            | “unsigned int”
    signed                  | “int”
    signed int              | “int”
    int                     | “int”
    unsigned short int      | “unsigned short int”
    unsigned short          | “unsigned short int”
    unsigned long int       | “unsigned long int”
    unsigned long           | “unsigned long int”
    unsigned long long int  | “unsigned long long int”
    unsigned long long      | “unsigned long long int”
    signed long int         | “long int”