term test1 result and Predicate of Induction

I got my term test1 result today. I felt not bad when I just finished the test because I knew how to do every question. However the grade was not good for me. I made a mistake that shouldn't have happened.

As we made a predicate in such form "P(n): For every n belongs to N,13^n-1 = 12y where y is also a natural number. We prove that for all n belongs to N, P(n) by Mathematical Induction". We define what P(n) exactly is in this question, then we indicate that for all n belongs to N,P(n) and what type of Induction would we use. However, I wrote "P(n): For all n belongs to N,  and all y belongs to N,13^n-1 = 12y." which is completely wrong because we should use INDUCTION to do it . Then we can't say all n belongs to N inside the definition of P(n).

It seems like a stupid mistake. The test consists of 3 question and 5 marks each. It cost me 1 mark for every question. So due to this little problem, I lost 20%! I am so depressed about it. =[. That is my fault. I will do better next time and I won't make such a low level mistake any more! I will do better next time.