Question

Use mathematical induction to prove that each proposition is valid for all positive integral values of n.

5^n + 3 is divisible by 4.

Answer 1

5^0+3 = 4

5^1 +3 = 8
5^2+3 = 5*5^1 + 3 = 4*5^1 +5+3 =28
5^3+3 = 5*5^2 + 3 = 4*25 + 5+3 = 128

5^(n+1) + 3 = 5 * 5^n + 3
= 4 *5^n + (5^n+3)
ah ha
4*5^n is divisible by 4 and so is (5^n+3)