$2005|(a^3+b^3) , 2005|(a^4+b^4 ) \implies2005|a^5+b^5$ How can I show that if $$2005|a^3+b^3 , 2005|a^4+b^4$$ then $$2005|a^5+b^5$$
I'm trying to solve them from $a^{2k+1} + b^{2k+1}=...$ but I'm not getting anywhere.
Can you please point in me the correct direction?
Thanks in advance

a triffle answer;we have $2005=401.5$ so $p=5,401$ also: $$a^5+b^5=(a+b)(a^4+b^4-ab(a^2-ab+b^2)) \tag I$$.also we have 
$$a^3+b^3=(a+b)(a^2-ab+b^2) \tag {II} $$  from the $p|a^3+b^3$ we have 2 cases :  1) if $p|a+b$ then  from $(I)$ we have $p|a^5+b^5$
2)if $p|(a^2-ab+b^2)$ by attention to $(II)$,$p|(-ab)(a^2-ab+b^2)$and therefore $p|a^5+b^5$ by(I) and $p|a^4+b^4$.$$$$
 next subsequent step is using definition of LCD:$2005=[401,5]|a^5+b^5$ .
