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  ã                   óŒ  • S r SSKJrJrJrJrJrJrJrJ	r	J
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JrJrJr  SSKJrJrJr  SSKJrJrJrJrJrJrJrJrJrJrJrJrJrJ r J!r!J"r"J#r#J$r$J%r%J&r&J'r'J(r(J)r)J*r*J+r+J,r,J-r-  SSK.J/r/  SSK0J1r1J2r2J3r3J4r4J5r5J6r6J7r7J8r8J9r9J:r:J;r;J<r<J=r=J>r>J?r?  SSK@JArAJBrBJCrC  SSKDJErEJFrFJGrGJHrHJDrD  SS	KIJJrJJIrIJKrK  SS
KLJLrL  SSKMJMrM  SSKNJNrNJOrO  / SQrPg)z$
Number theory module (primes, etc)
é   )Ú	nextprimeÚ	prevprimeÚprimeÚprimepiÚ
primerangeÚ	randprimeÚSieveÚsieveÚ	primorialÚcycle_lengthÚ	compositeÚcompositepi)ÚisprimeÚis_gaussian_primeÚis_mersenne_prime)ÚdivisorsÚproper_divisorsÚ	factorintÚmultiplicityÚmultiplicity_in_factorialÚperfect_powerÚfactor_cacheÚpollard_pm1Úpollard_rhoÚprimefactorsÚtotientÚdivisor_countÚproper_divisor_countÚdivisor_sigmaÚ	factorratÚreduced_totientÚprimenuÚ
primeomegaÚmersenne_prime_exponentÚ
is_perfectÚis_abundantÚis_deficientÚis_amicableÚis_carmichaelÚ	abundanceÚdraÚdrm)Únpartitions)Úis_primitive_rootÚis_quad_residueÚlegendre_symbolÚjacobi_symbolÚn_orderÚsqrt_modÚquadratic_residuesÚprimitive_rootÚnthroot_modÚis_nthpow_residueÚsqrt_mod_iterÚmobiusÚdiscrete_logÚquadratic_congruenceÚpolynomial_congruence)Úbinomial_coefficientsÚbinomial_coefficients_listÚmultinomial_coefficients)Úcontinued_fraction_periodicÚcontinued_fraction_iteratorÚcontinued_fraction_reduceÚcontinued_fraction_convergentsÚcontinued_fraction)Úcount_digitsÚdigitsÚis_palindromic)Úegyptian_fraction)Úecm)ÚqsÚ	qs_factor)Ir   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rF   rE   rG   rH   rI   rJ   rK   N)QÚ__doc__Úgenerater   r   r   r   r   r   r	   r
   r   r   r   r   Ú	primetestr   r   r   Úfactor_r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   Úpartitions_r-   Úresidue_ntheoryr.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   Úmultinomialr=   r>   r?   rD   r@   rA   rB   rC   rF   rE   rG   rH   rI   rJ   rK   Ú__all__© ó    ÚS/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/ntheory/__init__.pyÚ<module>rW      sš   ðñ÷M÷ M÷ Mó Mç DÑ D÷÷ ÷ ÷ ÷ ÷ ÷ ñ õ %÷>÷ >÷ >÷ >ñ >÷ñ ÷7õ 7÷ 9Ñ 8Ý 0Ý ß ò%�rU   