find all x such that x^3-x+1 is congruent to 0 mod 6.

i tried but it seems like there is no x

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- May 14th 2012, 03:21 PMalexandrabel90congruence
find all x such that x^3-x+1 is congruent to 0 mod 6.

i tried but it seems like there is no x - May 14th 2012, 05:11 PMHallsofIvyRe: congruence
You are right.

0^3- 0+ 1= 1

1^3- 1+ 1= 1

2^3- 2+ 1= 7= 1 mod 6

3^3- 3+ 1= 25= 1 mod 6

4^3- 4+ 1= 61= 1 mod 6

5^3- 5+ 1= 121= 1 mod 6

6^3- 6+ 1= 211= 1 mod 6

That's all you have to do. For all x, mod 6. - May 15th 2012, 01:35 AMSylvia104Re: Congruence
A little observation should tell you that is always odd and therefore can never be divisible by (Wink)

If you delve further, you have a product of three consecutive integers – this is always divisible by because it always contains exactly one multiple of and at least one multiple of Hence for all