should I present solution ideas in a cover letter?

I am in the process of applying for following doctoral studies in Computer Science, already communicated by one professor in charge of a research group and he asked me to write a cover letter. I have been reading into the literature about the research that they are doing, and I think I have figured a technique/algorithm that might be useful for what they are doing. The question that I have is that if I should stated in my cover letter that maybe for solving problem X that the research group is studying, they should apply technique Y and explain it why; should I put that? Or will it sound too confident to do that? (or maybe to ignorant, if I fail in my assumptions)

Thanks