Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers or defined as generalizations of the integers.
The Isley Brothers are an American family musical group originally from Cincinnati, Ohio, that started as a vocal trio consisting of brothers O'Kelly Isley Jr., Rudolph Isley and Ronald Isley in the 1950s. With a career spanning over eight decades, the group has enjoyed one of the "longest, most influential, and most diverse careers in the pantheon of popular music".
Sister Sledge is an American musical vocal group from Philadelphia, Pennsylvania. Formed in 1971, the group consisted of sisters Debbie, Joni, Kim, and Kathy Sledge. The siblings achieved international success at the height of the disco era. In 1979, they released their breakthrough album We Are Family, which peaked at number three on the Billboard 200 and included the 1979 US top-10 singles "He's the Greatest Dancer" and "We Are Family". A third single, "Lost in Music", reached the US top 40. "We Are Family" earned a Grammy Award nomination for Best R&B Performance by a Duo or Group with Vocal.
Lionel Brockman Richie Jr. is an American singer, songwriter, musician, record producer, and television judge. He rose to fame in the 1970s as a songwriter and the co-lead singer of funk band the Commodores; writing and recording the hit singles "Easy", "Sail On", "Three Times a Lady" and "Still", with the group before his departure. In 1980, he wrote and produced the US Billboard Hot 100 number one single "Lady" for Kenny Rogers. The following year, he wrote and produced the single "Endless Love", which he recorded as a duet with Diana Ross; it remains among the top 20 bestselling singles of all time, and the biggest career hit for both artists. In 1982, he officially launched his solo career with the album Lionel Richie, which sold over four million copies and spawned the singles "You Are", "My Love", and the number one single "Truly".
Purple Rain is the sixth studio album by American recording artist Prince, released on June 25, 1984, by Warner Bros. Records and the soundtrack to the 1984 film of the same name. Purple Rain was musically denser than Prince's previous albums, emphasizing full band performances, and multiple layers of guitars, keyboards, electronic synthesizer effects, drum machines, and other instruments.
Sheena Shirley Easton is a Scottish singer and actress. Easton came into the public eye in an episode of the first British musical reality television programme The Big Time: Pop Singer, which recorded her attempts to gain a record contract and her eventual signing with EMI Records.
Thriller is the sixth studio album by the American singer and songwriter Michael Jackson, released on November 30, 1982, by Epic Records. It was produced by Quincy Jones, who had previously worked with Jackson on his 1979 album Off the Wall. Jackson wanted to create an album where "every song was a killer". With the ongoing backlash against disco music at the time, he moved in a new musical direction, resulting in a mix of pop, post-disco, rock, funk, and R&B sounds. Thriller foreshadows the contradictory themes of Jackson's personal life, as he began using a motif of paranoia and darker themes. Paul McCartney appears on "The Girl Is Mine", the first credited appearance of a featured artist on a Michael Jackson album. Recording took place from April to November 1982 at Westlake Recording Studios in Los Angeles, California, with a budget of $750,000.
James Edward Ingram was an American singer, songwriter, record producer, and instrumentalist. He was a two-time Grammy Award-winner and a two-time Academy Award nominee for Best Original Song. After beginning his career in 1973, Ingram charted eight Top 40 hits on the U.S. Billboard Hot 100 chart from the early 1980s until the early 1990s, as well as thirteen top 40 hits on the Hot R&B/Hip-Hop Songs chart. In addition, he charted 20 hits on the Adult Contemporary chart. He had two number-one singles on the Hot 100: the first, a duet with fellow R&B artist Patti Austin, 1982's "Baby, Come to Me" topped the U.S. pop chart in 1983; "I Don't Have the Heart", which became his second number-one in 1990 was his only number-one as a solo artist.
Sade are an English band, formed in London in 1982 and named after its lead singer, Sade Adu. Three of its members were originally from Hull in the East Riding of Yorkshire. Its music features elements of soul, quiet storm, smooth jazz and sophisti-pop. All of its albums, including compilations and a live album, have charted in the US Top Ten.
"In the Midnight Hour" is a song originally performed by Wilson Pickett in 1965 and released on his 1965 album of the same name, also appearing on the 1966 album The Exciting Wilson Pickett. The song was composed by Pickett and Steve Cropper at the historic Lorraine Motel in Memphis, later the site of the assassination of Martin Luther King Jr. Pickett's first hit on Atlantic Records, it reached number one on the R&B charts and peaked at number 21 on the pop charts.
"Let's Stay Together" is a song by American singer Al Green from his 1972 album of the same name. It was produced and recorded by Willie Mitchell, and mixed by Mitchell and Terry Manning. Released as a single in 1971, "Let's Stay Together" reached number 1 on the Billboard Hot 100, and remained on the chart for 16 weeks and also topped Billboard's R&B chart for nine weeks. Billboard ranked it as the number 11 song of 1972.
The S.O.S. Band is an American R&B and electro-funk group who gained fame in the 1980s. They are best known for the songs "Take Your Time ", "Just Be Good to Me", and "The Finest".
"I Just Called to Say I Love You" is a ballad written, produced, and performed by American R&B singer and songwriter Stevie Wonder. It was a major international hit, and remains Wonder's best-selling single to date, having topped a record 19 charts.
Billboard Year-End charts are a cumulative measure of a single or album's performance in the United States, based upon the Billboard magazine charts during any given chart year. Billboard's "chart year" runs from the first Billboard "week" of December to the final week in November, but because the Billboard week is dated in advance of publication, the last calendar week for which sales are counted is usually the third week in November. This altered calendar allows for Billboard to calculate year-end charts and release them in time for its final print issue in the last week of December.
"It's All in the Game" is a pop song whose most successful version was recorded by Tommy Edwards in 1958. Carl Sigman composed the lyrics in 1951 to a wordless 1911 composition titled "Melody in A Major", written by Charles G. Dawes, who was later Vice President of the United States under Calvin Coolidge. It is the only No. 1 single in the U.S. to have been co-written by a U.S. Vice President or a Nobel Peace Prize laureate.
"Hello" is a song by American singer and songwriter Lionel Richie. Taken as the third single from his second solo album, Can't Slow Down (1983), the song was released in 1984 and reached number one on three Billboard music charts: the pop chart, the R&B chart, and the Adult Contemporary chart. The song also went to number one on the UK Singles Chart for six weeks.
"She's Strange" is a 1984 single by the R&B/funk band, Cameo released in 1984. It is the title track from their tenth album. The single was their first to top the R&B chart, hitting number one for four weeks in April 1984. The single was the band's first to reach the Billboard Hot 100 pop chart, peaking at number forty-seven. The video was directed by Dieter 'Dee' Trattmann.
A light-year, alternatively spelled lightyear, is a large unit of length used to express astronomical distances and is equivalent to about 9.46 trillion kilometers (9.46×1012 km), or 5.88 trillion miles (5.88×1012 mi). As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in a vacuum in one Julian year (365.25 days). Because it includes the time-measurement word "year", the term light-year is sometimes misinterpreted as a unit of time.
"She's Trouble", also known as "Trouble", is a song by Michael Jackson, recorded in 1981 and originally written for his Thriller LP. However, Jackson's original version was an outtake and therefore never released, either as a single or an album cut.