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# prove that 5 does not divide a^3+a^2+1 watch

1. as title says

cheers
2. Consider the various values which a can take (mod 5)
3. (Original post by SimonM)
Consider the various values which a can take (mod 5)
so basically you mean something like

a^3=-a^2-1(mod 5) seems wrong though

bit confused still
4. No, I meant plug in a = 0,1,2,3,4 and seeing if it is ever zero. If it isn't you're fine
5. All Z can be split into 5 congruence classes, as simon says these are 0,1,2,3,4 (mod 5). Hence looking at these 5 values for a, will infact be looking at the whole range of every possibly integer.

so 0^3+0^2+1 doesn't equal 0mod5
1^3+1^2+1 doesn't equal 0mod5

etc etc.
6. thanks guys i get it now

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Updated: January 21, 2010
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