Find the least pssible value of , where are positive integers such that divides and divides .

Follow Math Help Forum on Facebook and Google+

Originally Posted by alexmahone Find the least possible value of , where are positive integers such that divides and divides . I make the answer 28 (a=23, b=5), but I don't have a neat argument to prove that it's minimal.

Originally Posted by Opalg I make the answer 28 (a=23, b=5), but I don't have a neat argument to prove that it's minimal. here's a proof: and are equivalent to say that and for some integers clearly we must have: we also get: so: hence: which gives us: clearly implies if then since we will have: thus: if then also from we get: thus the minimum possible value of is therefore:

Last edited by NonCommAlg; Oct 18th 2008 at 10:51 PM.