Proving with Congruence of intergers

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To prove that b^3 + b^2 + 1 does not divide by 5, it is essential to show that it is not congruent to 0 modulo 5. The approach involves using contradiction, but clarity on how to apply this method is needed. Exploring all cases from 0 to 4 modulo 5 can provide insight into the proof. The discussion highlights uncertainty about the contradiction method and suggests that alternative methods may also be viable. Ultimately, confirming the non-divisibility by testing these cases is a practical approach.
doggie_Walkes
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It just how do i prove that

b^3 +b^2 +1 does not divide by 5


Im thinking this way,
cause i know that b^3 +b^2 +1 is not congruent to 0(mod5)

therefore we use contradition to prove it. I am just not sure how to use contradition? or maybe I am looking at this in a completely bad light? maybe there is another method?
 
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This can be worked out by considering all the cases from 0 to 4 mod 5.
 
Double posted.
 

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