Is there a pattern of thinking that could make me better at solving

Yes. You start by not posting /pol/ shit

>>8956842
First pic I clicked on, didn't even look

>>8956842
Stop being a commie.

>>8956848
Make me, big boy

>>8956848
No, he actually has a point. If you really want to develop good habits of thought for mathematics, then don't spend so much time on /pol/ where the highest levels of discussion is memes and ad hominem attacks

>>8956837
These are the steps of problem solving at the highest level

1) Categorize the problem
Sometimes the kind of problem it is is obvious but other times it is not that obvious so you should be able to see a problem and immediately imagine what kind of problem it is and how to solve it.
2) Quick attack
After you have categorized the problem you should have a mental list of quick weapons that you throw at any problem of the kind you have identified. The usual ones are first, rewrite whatever algebraic statements you have in all their alternative forms. A second one is seeing what the contradiction hypothesis is and judging if the contradiction hypothesis is stronger than the hypothesis. (In other words, if you have to prove that x > y then quickly see what would happen if you assume y > x and see if that looks more promising for a quick argument)
3) Trial and error
If the quick attack did not yield any easy answers, or yielded only minor results, it is time to do soft but more calculated attacks. In the case that you have a diophantine equation, try to quickly find some example solutions. Try to find all trivial solutions too if you can. In other case. Try to extract new information out of trial and error and then try to use that new information with the previous quick attack techniques you used
4) Final conjecture and proof
Now that you have extracted all possible information, it is time for you to make a conjecture. This should be something that is equivalent to what you want to prove, but also more graphic and intuitive. You should be able to do this because in the previous step you potentially found new information that can easily enrich the problem's statement if you know how to incorporate it. And now you prove that.

>>8956865
>and now you prove that

Lol 2ez4u