Also any recommended books to read for research please. I have a few of the best books at home, e.g. tom.m.apostol "Introduction to analytic number theory",, m.ram.murty "Problems in analytic number theory", S.U.M.S "Elementary number theory" 104 number theory problems (this one is mainly competition based), "Introduction to number theory" from the UKMT series (obviously also competition based), and "the higher arithmetic" by H davenport. Please don't ignore. Someone with a good background knowledge in maths please reply!