Exercises
6. Show that if a 2+ b = c2, then 3jab. 7. Show that 1 + 1 2 + 1 3 + + 1 n can never be an integer for n 2. 8. Let f(n) denote the sum of the digits of n. Let N= 44444444. Find f(f(f(N))). 9. Show that there exist 2020 consecutive numbers, each of which is divisible by a cube greater than 1. 10. Find all triples of positive integers (a;b;c ... ................
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