Question: Who encouraged Lennon and McCartney to write a song?
About the article "I Want to Hold Your Hand", section "Background and composition".

Candidate passages:
Although it is said that Brian Epstein had encouraged Lennon and McCartney to write a song to appeal to American listeners this has been denied by George Martin.
McCartney had recently moved into 57 Wimpole Street, London, where he was living as a guest of Dr Richard and Margaret Asher, whose daughter, actress Jane Asher, had become McCartney’s girlfriend after meeting him earlier in the year.
This location briefly became Lennon and McCartney's new writing base, taking over from McCartney’s Forthlin Road home in Liverpool.
Margaret Asher taught the oboe in the "small, rather stuffy music room" in the basement where Lennon and McCartney sat at the piano and composed 'I Want to Hold Your Hand'.
In September 1980, Lennon told "Playboy" magazine:In 1994, McCartney agreed with Lennon's description of the circumstances surrounding the composition of "I Want to Hold Your Hand", saying:
Lennon–McCartney (also written Lennon/McCartney and occasionally known as McCartney–Lennon) is a rock music songwriting partnership between English vocalists John Lennon (October 9, 1940December 8, 1980) and Paul McCartney (born June 18, 1942) of The Beatles.
It is one of the best-known and most successful musical collaborations in history.
Between 1962 and 1969, the partnership published approximately 180 jointly credited songs, of which the vast majority were recorded by the Beatles, forming the bulk of their catalogue.
Unlike many songwriting partnerships that comprise separate lyricist and composer, both Lennon and McCartney wrote words and music.
Sometimes, especially early on, they would collaborate extensively when writing songs, working "eyeball to eyeball".
Later, it became more common for one of the two credited authors to write all or most of a song with limited input from the other.
""He provided a lightness, an optimism, while I would always go for the sadness, the dischords, the bluesy notes"", John Lennon explained in his 1980 Playboy interviews.
By an agreement made before the Beatles became famous, Lennon and McCartney were credited equally with songs that either one of them wrote while their partnership lasted.
Lennon–McCartney compositions have been the subject of numerous cover versions.
According to Guinness World Records, "Yesterday" has been recorded by more artists than any other song. 
The song's lyrics describe the titular "fool", a solitary figure who is not understood by others, but is actually wise.
McCartney said the song relates to someone like Maharishi Mahesh Yogi:Alistair Taylor, in the book "Yesterday", reports a mysterious incident involving a man who inexplicably appeared near him and McCartney during a walk on Primrose Hill and then disappeared again, soon after McCartney and Taylor had conversed about the existence of God; this allegedly prompted the writing of the song.
McCartney played the song for John Lennon during a writing session for "With a Little Help from My Friends", and Lennon told him to write it down.
McCartney did not; he was sure he would not forget it.
In his 1980 interview with "Playboy", Lennon said, "Now that's Paul.
Another good lyric.
Shows he's capable of writing complete songs."
"The Night Before" is a song by the Beatles from the album and film "Help!".
It was written by Paul McCartney and credited to Lennon–McCartney. 
"I'm Down" is a song by the Beatles written by Paul McCartney (credited to Lennon–McCartney) and first released as the B-side to the single "Help!"
in 1965.