Hello everyone. I'm trying to set this problem up to prove by induction but having some issues. Suppose that for some Predicate P(k), you first prove that P(1) is true, and then you do the following. You prove that, for every positive even integer k, if P(i) is true for all odd integers i such that 0 < i < k, then P(k+1) is true. For which values of n can you now be certain that P(n) is true? Give an explanation of why your answer is correct. Hint: you have to "unwind the meaning of the first paragraph" So am i suppose to actually prove that for every positive even integer k, if P(i) is true for all odd integers i such that 0 < i < k, then P(k+1) is true. Then test the base case to make sure p(1) is true? And if that is true, then I have to go on to prove that P(1)->P(2) P(2)->P(3) P(3)->P(4) P(n)->P(n+1) ? Am I suppose to be using Strong mathematical induction or just regular? P(n) makes me think i have to use strong, because in those they usually start out with, Let the property P(n) be the inequality or statment.... So could i write: Let the Property P(n) be 2k+1, where k is any postive integer >= 1. #this would be the definition of an odd number. But I still don't see what i'm proving. Usually I'm proving 2 statements are equivlent to eachother in regular induction. ANd in strong induction Ive only been proving things in a sequence so i'm confused on how to set this up and the book had no examples of this type. Any help would be great! Thanks!