
    sg                         d dl mZ d dl mZ d dlmZ d dlmZmZ d dl	m
Z
  e ej                  dd            d	        Z e ej                  dd            d
        Zy)    )given)
strategies)divisors)divisor_sigmatotient)	is_square   l    d(	 )nc                 J   t        |       }t        |      }t        |       |dz  dk(  k(  sJ |D cg c]  }t        |       }}|D cg c]  }t	        | |z         }}t        ||      D cg c]
  \  }}||z   }}}| |z  t        |      k(  sJ y c c}w c c}w c c}}w )N   r	   )r   lenr   r   r   zipsum)	r
   divtau_nisigmastotientsabmuls	            V/var/www/html/venv/lib/python3.12/site-packages/sympy/ntheory/tests/test_hypothesis.pytest_tau_hypothesisr      s    
1+CHEQ<EAIN+++(+,1mA,F,),-AQ-H- 2
3TQ1q5
3C
3u9C    --
3s   B	B/Bc                     t        |       | k  sJ t        |       }|D cg c]  }t        |       }}| t        |      k(  sJ y c c}w )N)r   r   r   )r
   r   r   r   s       r   test_totient_hypothesisr      sI    1:??
1+C$'(q
(H(H )s   AN)
hypothesisr   r   stsympyr   %sympy.functions.combinatorial.numbersr   r   sympy.ntheory.primetestr   integersr   r        r   <module>r$      s`     '  H - Q	 ! !! Q	  !r#   