Patulong po

Theory of Numbers Problem Set 3 Prove the following using mathematical induction. 1. 32n - 1 is divisible by 8 for all natural number n. 2. 10n+ 3(4n+2) + 5 is divisible by 9 for all positive integral values of n 3. n3 + 6n2 - 4n + 3 is divisible by 3 for any natural number n. 4. 72n - 48n - 1 is divisible by 2304 for every natural integer n. 5. a2n-1 + ban-1 is divisible by a + b, for n is a positive integer