The text fills a last greater gap in the sequence of the author's basic studies in number theory. Integers with or without special characteristics can be represented by integer sum functions of one or more natural numbers, which may be primes or composite numbers. In only few cases, there can be direct methods for finding solutions to equations or tests for the possibility of solutions. Within the latter, congruences of numbers or functions can be regarded.In seven chapters, binary quadratic forms of two variables, general quadratic forms and algorithms, remarks about general forms, theoretical and practical representations of natural numbers, some useful congruences, and Goldbach's Conjecture are discussed. After the text, a choice of literature, collected corrections to former books of the author, and a complete index are given.