[tetris11]

probably easier in bash:

    number="$1"
    if [[ "$number" =~ "^(2|4|6|8|10|12|14|16|18|20)$" ]]; then
        echo even
    elif [[ "$number" =~ "^(1|3|5|7|9|11|13|15|17|19)$" ]]; then
        echo odd
    else
        echo Nan
    fi

A bit limited, but you can scale it up

[teo_zero]

Scaled up:

  case "$1" in
    *0|*2|*4|*6|*8) echo even;;
    *) echo odd;;
  esac

If $1 had a trailing non-digit, or was empty, that would indeed be an odd situation!