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  ã                   ó®  € R t ^RIHtHtHtHtHtHtHtH	t	H
t
HtHtHt ^RIHtHtHt ^RIHtHtHtHtHtHtHtHtHtHtHtHtHtH t H!t!H"t"H#t#H$t$H%t%H&t&H't'H(t(H)t)H*t*H+t+H,t,H-t- ^RI.H/t/ ^RI0H1t1H2t2H3t3H4t4H5t5H6t6H7t7H8t8H9t9H:t:H;t;H<t<H=t=H>t>H?t? ^RI@HAtAHBtBHCtC ^RIDHEtEHFtFHGtGHHtHHDtD ^RIIHJtJHItIHKtK ^R	ILHLtL ^R
IMHMtM ^RINHNtNHOtO . RNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNR NR!NR"NR#NR$NR%NR&NR'NR(NR)NR*NR+NR,NR-NR.NR/NR0NR1NR2NR3NR4NR5NR6NR7NR8NR9NR:NR;NR<NR=NR>NR?NR@NRANRBNRCNRDNRENRFNRGNRHNRINRJNRKNRLNRMNRNNRONRPNRQNRRNRSNRTNtPRU# )Vz$
Number theory module (primes, etc)
)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_factorr   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$   r%   r&   r'   r(   r)   r*   r+   r   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rE   rD   rF   rG   rH   rI   rJ   N)QÚ__doc__Úgenerater   r   r   r   r   r   r   r	   r
   r   r   r   Ú	primetestr   r   r   Úfactor_r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   Úpartitions_r,   Úresidue_ntheoryr-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   Úmultinomialr<   r=   r>   rC   r?   r@   rA   rB   rE   rD   rF   rG   rH   rI   rJ   Ú__all__© ó    ÚT/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/ntheory/__init__.pyÚ<module>rV      sq  ðñ÷M÷ M÷ Mó Mç DÑ D÷÷ ÷ ÷ ÷ ÷ ÷ ñ õ %÷>÷ >÷ >÷ >ñ >÷ñ ÷7õ 7÷ 9Ñ 8Ý 0Ý ß ð%Øð%Øð%Ø%ð%Ø'0ð%Ø2>ð%Ø@Kð%àð%àð%à!ð%à#1ð%à3>ð%à@Mð%ð ð	%ð #ð	%ð %8ð	%ð ð%ð "ð%ð $/ð%ð 1?ð%ð APð%ð ð%ð "ð%ð $1ð%ð 3Að%ð CLð%ð ð%ð ,ð%ð .=ð%ð ?Jð%ð ð%ð !ð%ð #/ð%ð 1Jð%ð ð%ð  ð%ð "0ð%ð 2?ð%ð ð%ð !ð%ð #(ð%ð */ð%ð 1Lð%ð ð%ð  ð!%ð  +ð!%ð  ->ð!%ð" ð#%ð" ð#%ð" !+ð#%ð" -Að#%ð$ ð%%ð$ $ð%%ð$ &9ð%%ð$ ;Jð%%ð& ð'%ð& ð'%ð& 5ð'%ð& 7Nð'%ð* ð+%ð* :ð+%ð, ð-%ð0 "ð1%ð0 $Að1%ð2  ð3%ð2 "Bð3%ð4 ð5%ð8 ð9%ð: ð;%ð< ð=%ð@ ðA%ðD 
ðE%ðH 	ðI%ðH ðI%‚rT   