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The 180th meridian is an imaginary line of longitude located at 180 degrees east or west of the Prime Meridian, which is defined as 0 degrees longitude. It is essentially the opposite side of the Earth from the Prime Meridian. The 180th meridian runs from the North Pole to the South Pole and largely follows the line of the International Date Line. It passes through the Pacific Ocean and divides the Eastern and Western Hemispheres.

In number theory, "effective results" refer to theorems or results that not only provide qualitative information (e.g., existence, properties, etc.) about mathematical objects but also yield explicit methods, algorithms, or bounds that allow for the computation of specific examples or the verification of claims. Essentially, an effective result provides a concrete way to achieve or demonstrate what a more abstract result asserts.