solve in Z : http://www.gnux.be/latex/data/176b39...5e3585e69a.png

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- Jun 2nd 2009, 01:11 PMdhiabModulo 42
- Jun 2nd 2009, 03:32 PMDeadstar
(not sure what the latex symbol is for equivalent)

so n=1 or -2 which is equivalent to 1 and 40 in mod 42. - Jun 2nd 2009, 03:43 PMTheEmptySet
- Jun 2nd 2009, 06:00 PMTheAbstractionist
Hi

**dhiab**.

Unfortunately,**Deadstar**and**TheEmptySet**miss two solutions:

If 2, 3, 7 all divide or , the solution set is

Otherwise …

(i) If 2, 3 divide and 7 divides then The Chinese-remainder method (or otherwise trial and error) gives as one solution. Hence the solution set is

(ii) If 3 divides and 2, 7 divide then In this case, but we already have this solution above.

(iii) If 2 divides and 3, 7 divide then which gives the same solution set as in (i).

(iv) If 2, 7 divide and 3 divides then So which we already have above.

(v) If 3, 7 divide and 2 divides then So and we have found a new solution set.

(vi) Finally, if 7 divides and 2, 3 divide then and again we have

Hence the complete solution set is