Determine what is wrong with the given induction arguments. We will prove that 5 divide...

Determine what is wrong with the given induction arguments.

We will prove that 5 divides 5n + 3 for all positive integers n.

Assume that, for some positive integer k, 5 divides 5k + 3. Then there is a positive integer p such that 5k + 3 = 5p. now

Since 5 divides 5(p + 1), it follows that 5 divides 5(k + 1) + 3, which is the statement that we want to prove.

Hence, by the principle of mathematical induction, 5 divides 5n + 3 for all positive integers n.