For historical reasons and in order to have application to the solution of Diophantine equations, results in number theory have been scrutinised more than in other branches of mathematics to see if their content is effectively computable[citation needed].
The requirement of computability is reflected in and contrasts with the approach used in the analytic number theory to prove the results.
In other words, if it were known that there was M > N with a change of sign and such that for some explicit function G, say built up from powers, logarithms and exponentials, that means only for some absolute constant A.
The value of A, the so-called implied constant, may also need to be made explicit, for computational purposes.
Many of the principal results of analytic number theory that were proved in the period 1900–1950 were in fact ineffective.