SOLUTION: Prove: Let p(sub1),p(sub2),...,p(sub n)be primes. Then, p(sub1) x p(sub2) x ... x p(sub n)+ 1 is not divisible by any of these primes. (x indicates mult

Question 400874: Prove: Let p(sub1),p(sub2),...,p(sub n)be primes. Then, p(sub1) x p(sub2) x ... x p(sub n)+ 1 is not divisible by any of these primes. (x indicates multiplication)
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Let k = (p_1)(p_2)(p_3)...(p_n). It follows that each of these n primes divides k, so k ≡ 0 (mod p_i) for all . Hence, k+1 is congruent to 1 (mod p_i) for all p_i, and k+1 cannot divide any of these primes (for k+1 to be divisible by some prime, k+1 must be congruent to at least 2 modulo p_i).
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