
    \h                         S SK Jr  S SK Jr  S SKJr  S SKJrJr  S SK	J
r
  \" \R                  " SS5      S9S	 5       r\" \R                  " SS5      S9S
 5       rg)    )given)
strategies)divisors)divisor_sigmatotient)	is_square   l    d(	 )nc                 V   [        U 5      n[        U5      n[        U 5      US-  S:H  :X  d   eU Vs/ s H  n[        U5      PM     nnU Vs/ s H  n[	        X-  5      PM     nn[        XE5       VVs/ s H	  u  pgXg-  PM     nnnX-  [        U5      :X  d   eg s  snf s  snf s  snnf )N   r	   )r   lenr   r   r   zipsum)	r
   divtau_nisigmastotientsabmuls	            [/var/www/auris/envauris/lib/python3.13/site-packages/sympy/ntheory/tests/test_hypothesis.pytest_tau_hypothesisr      s    
1+CHEQ<EAIN+++(+,1mAF,),-AH- 2
32TQ152C
39C    --
3s   BB 4B%c                     [        U 5      U ::  d   e[        U 5      nU Vs/ s H  n[        U5      PM     nnU [        U5      :X  d   eg s  snf )N)r   r   r   )r
   r   r   r   s       r   test_totient_hypothesisr      sJ    1:??
1+C$'(Cq
CH(H )s   A
N)
hypothesisr   r   stsympyr   %sympy.functions.combinatorial.numbersr   r   sympy.ntheory.primetestr   integersr   r        r   <module>r$      s\     '  H - Q	 ! !! Q	  !r#   