Question 1. Let a, b, c be 3 distinct numbers from {1, 2, 3, 4, 5, 6}. Show that 7 divides abc + (7 − a)(7 − b)(7 − c). Question 2. Show that there is a natural number n such that the number a = n! ends exacly in 2009 zeros.
Question 1. Let a, b, c be 3 distinct numbers from {1, 2, 3, 4, 5, 6}. Show that 7 divides abc + (7 − a)(7 − b)(7 − c).
Question 2. Show that there is a natural number n such that the number a = n! ends exacly in 2009 zeros.
