some short and selected math problems of different levels in random order I try to keep the ans simple
Saturday, August 5, 2017
2017/015) Show that there are infinitely many n such that 6n+1 and 6n-1 are both are composites
we have for n > 2 n^3-1= (n-1)(n^2+n+1) is composite and n^3+1=(n+1)(n^2-n+1) is composite for n ,
so if we choose n= 36m^3 we get 6n-1= (6m)^3-1 and 6n+1= (6m)^3 + 1 composites
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