It is useful for proving results about the normal order of an arithmetic function.

In prime number theory, they proved results and some notable conditional results.

He also proved similar results for 6 and 8 squares.

Techniques and methods from one area can be applied to prove results in a related area.

It proved excellent results within five years, and every other state took it as role model.

Studies on apes however have proven more advanced results in imitation, being able to remember and learn from what they imitate.

He proved important results concerning the invariants of the class groups of quadratic number fields.

In later chapters we shall prove several results of the above type where the symbols used will not necessarily stand for integers.

In quite a few cases, including that of the Weil conjectures, other methods have been found to prove such results unconditionally.

He specialized in number theory and analysis, and proved several results that eluded even Gauss.