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Cheyenne ( shy-AN or shy-EN) is the capital and most populous city of the U.S. state of Wyoming, as well as the county seat of Laramie County, with 65,132 residents, per the 2020 census. It is the principal city of the Cheyenne metropolitan statistical area which encompasses all of Laramie County and had 100,512 residents as of the 2020 census. Local residents named the town for the Cheyenne Native American people in 1867 when it was founded in the Dakota Territory. Along with Oklahoma City, Oklahoma and Topeka, Kansas, Cheyenne is one of three state capitals with an indigenous name in a state with an indigenous name. Cheyenne is the northern terminus of the extensive Southern Rocky Mountain Front, which extends southward to Albuquerque, New Mexico, and includes the fast-growing Front Range Urban Corridor. Cheyenne is situated on Crow Creek and Dry Creek.

Wyoming ( wye-OH-ming) is a landlocked state in the Mountain West subregion of the Western United States. It borders Montana to the north and northwest, South Dakota and Nebraska to the east, Idaho to the west, Utah to the southwest, and Colorado to the south. With a population of 576,851 in 2020, Wyoming is the least populous state despite being the 10th largest by area, with the second-lowest population density after Alaska. The state capital and most populous city is Cheyenne, which had a population of 65,132 in 2020. Wyoming's western half consists mostly of the ranges and rangelands of the Rocky Mountains; its eastern half consists of high-elevation prairie, and is referred to as the High Plains. Wyoming's climate is semi-arid in some parts and continental in others, making it drier and windier overall than other states, with greater temperature extremes. The federal government owns just under half of Wyoming's land, generally protecting it for public uses. The state ranks sixth in the amount of land—and fifth in the proportion of its land—that is owned by the federal government. Its federal lands include two national parks (Grand Teton and Yellowstone), two national recreation areas, two national monuments, and several national forests, as well as historic sites, fish hatcheries, and wildlife refuges. Indigenous peoples inhabited the region for thousands of years. Historic and currently federally recognized tribes include the Arapaho, Crow, Lakota, and Shoshone. Part of the land that is now Wyoming came under American sovereignty via the Louisiana Purchase, part via the Oregon Treaty, and, lastly, via the Mexican Cession. With the opening of the Oregon Trail, the Mormon Trail, and the California Trail, vast numbers of pioneers travelled through parts of the state that had once been traversed mainly by fur trappers, and this spurred the establishment of forts, such as Fort Laramie, that today serve as population centers. The Transcontinental Railroad supplanted the wagon trails in 1867 with a route through southern Wyoming, bringing new settlers and the establishment of founding towns, including the state capital of Cheyenne. On March 27, 1890, Wyoming became the union's 44th state. Farming and ranching, and the attendant range wars, feature prominently in the state's history. Today, Wyoming's economy is largely based on tourism and the extraction of minerals such as coal, natural gas, oil, and trona. Its agricultural commodities include barley, hay, livestock, sugar beets, wheat, and wool. Wyoming was the first state to allow women the right to vote (not counting New Jersey, which had allowed it until 1807), and the right to assume elected office, as well as the first state to elect a female governor. In honor of this part of its history, its most common nickname is "The Equality State" and its official state motto is "Equal Rights". It is among the least religious states in the country, and is known for having a political culture that leans towards libertarian conservatism. The Republican presidential nominee has carried the state in every election since 1968.