SOLUTION: Determine all integers k such that {{{k^3+k+1}}} is divisible by 11.

Question 1019201: Determine all integers k such that is divisible by 11.
Answer by Edwin McCravy(20065) (Show Source): You can put this solution on YOUR website!



We see that when k=2



And if we add any multiple of 11 to 2,



We get



which is  plus some multiples of 11,

so integers of the form 2+11n, when n is a non-
negative integer, substituted for k into  
will always yield a number divisible by 11.

They are the positive integers 2 mod 11.

Edwin

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