Use the formula y = (x-y)(x-+x-2y+...+xy-2+y-) to deduce that if 2 1 is prime, then n...

 

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Use the formula "y" = (x-y)(x-¹+x-2y+...+xy"-2+y"-¹) to deduce that if 2" 1 is prime, then n is necessarily prime. The primality of n is however not also sufficient. Check that for n = 11 the corresponding 211 - 1 is not prime. Use the formula "y" = (x-y)(x-¹+x-2y+...+xy"-2+y"-¹) to deduce that if 2" 1 is prime, then n is necessarily prime. The primality of n is however not also sufficient. Check that for n = 11 the corresponding 211 - 1 is not prime.

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To deduce that if 2k 1 is prime then n is necessarily prime we can start by substituting n 2k 1 int... View the full answer