hasManyThroughrelationship return wrong SQL sentence - php

Question

I would like to get some data for tables that dont have a directly relation. The context is the following:
//** account_table **// Normal user, who can buy any book
account_id
account_info
//** book_table **// Books
book_id
account_id
author_id
//** author_table **// Author, who can write a lot of books (they will have more functions, this is the why i choose to create other table)
author_id
book_id
author_desc
The models that im using are:
class Account extends Eloquent implements UserInterface, RemindableInterface {
protected $table = 'account_table';
protected $primaryKey = 'account_id';
public function Book()
{
return $this->hasMany('Book', 'account_id');
}
public function Author()
{
return $this->hasManyThrough('Author', 'Book','account_id','book_id');
}
}
class Book extends Eloquent implements UserInterface, RemindableInterface {
protected $table = 'book_table';
protected $primaryKey = 'book_id';
public function Account()
{
return $this->belongsTo('Account','account_id');
}
public function Author()
{
return $this->hasOne('Author', 'author_id', 'author_id');
}
}
class Author extends Eloquent implements UserInterface, RemindableInterface {
protected $table = 'author_table';
protected $primaryKey = 'author_id';
public function Book()
{
return $this->belongsToMany('Book', 'author_id');
}
}
So to get this information i use the following code:
$user = Account::find(166); //user
dd($user->Author);
The ouput throw an error like this:
SQLSTATE[42S22]: Column not found: 1054 Unknown column 'book.id' in 'on clause' (SQL: select `author_table`.*, `book_table`.`account_id` from `author_table` inner join `book_table` on `book_table`.`id` = `author_table`.`book_id` where `book_table`.`account_id` = 166)
Seems that it is looking for a field (id) that does not exist in my database, however i have defined all primaryKeys in the models. What should i do to get author_desc information in this context ?
EDIT (other example):
When i use the following code it retrieve the same error:
$user = Account::find(166);
echo Book::find(3);

Answer 1

You've defined a one-to-one relationship of Book to Author with the hasOne() method and a many-to-many relationship between Author and Book with the belongsToMany() method. These should be inverse relationships, instead. Try replacing the belongsToMany()method with the belongsTo() method. Something like this:
class Account extends Eloquent implements UserInterface, RemindableInterface {
protected $table = 'account_table';
protected $primaryKey = 'account_id';
public function Book()
{
return $this->hasMany('Book', 'account_id');
}
public function Author()
{
return $this->hasManyThrough('Author', 'Book','account_id','book_id');
}
}
class Book extends Eloquent implements UserInterface, RemindableInterface {
protected $table = 'book_table';
protected $primaryKey = 'book_id';
public function Account()
{
return $this->belongsTo('Account','account_id');
}
public function Author()
{
return $this->hasOne('Author', 'author_id', 'author_id');
}
}
class Author extends Eloquent implements UserInterface, RemindableInterface {
protected $table = 'author_table';
protected $primaryKey = 'author_id';
public function Book()
{
return $this->belongsTo('Book', 'author_id');
}
}