It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that he (peace and blessings be upon him) said: "Whoever performs ablution, let him blow his nose, and whoever uses stones (to clean himself), let him use an odd number."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 235
Asim bin Laqit bin Sabirah narrates from his father that he and a companion of his came to Sayyidah Aishah (may Allah be pleased with her); they were looking for the Messenger of Allah (peace and blessings be upon him), but they did not find him, so Sayyidah Aishah (may Allah be pleased with her) fed them dates and 'asidah (a flour pudding). They had not stayed long when the Messenger of Allah (peace and blessings be upon him) arrived, walking in a dignified manner, and said: "Has anyone fed you two anything?" I said: Yes, O Messenger of Allah! Then I said: O Messenger of Allah! Tell us about the prayer. He (peace and blessings be upon him) said: "Perform ablution thoroughly, pass (water) between the fingers, and when you sniff water into your nose, do so deeply, but not while fasting."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 236
It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) commanded "rinsing the mouth and sniffing water into the nose."
(b) Sometimes the narrator narrates this hadith as mursal, leaving out Sayyiduna Abu Hurayrah (may Allah be pleased with him). The Shaykh says: In my estimation, he narrated it once as mursal and another time as connected (mawsul).
(c) Dawud bin al-Muhabbar also corroborates them in narrating it as connected. Apart from them, all the other narrators narrate it as mursal.
(d) The Shaykh (may Allah have mercy on him) says: Ibrahim bin Sulayman al-Khallal, a teacher of Ya'qub bin Sufyan, contradicted them both, narrating it from Hammad, from Ammar, from Sayyiduna Ibn Abbas (may Allah be pleased with them both); and both versions are not preserved (ghayr mahfuz).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 238
(a) It is narrated from Sayyidah Aishah (may Allah be pleased with her) that the Messenger of Allah (peace and blessings be upon him) said: "Rinsing the mouth and sniffing water into the nose are obligatory in ablution."
(b) Isma'il bin Bishr al-Balkhi also narrated it from Isam in the same way, except that he said: "(They are) part of the ablution without which the prayer is not complete."
(c) Sulayman bin Musa narrates it mursal from the Prophet (peace and blessings be upon him): "Whoever performs ablution, let him rinse his mouth and sniff water into his nose."
Isam is alone in narrating it (this way) and erred in it; the correct version is from Ibn Jurayj, from Sulayman bin Musa, as mursal.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 239
Sulayman bin Musa (may Allah have mercy on him) says that the Messenger of Allah (peace and blessings be upon him) said: "Whoever performs ablution, let him rinse his mouth and sniff water into his nose."
Muhammad bin al-Azhar is da'if (weak); this (connected version) is a mistake, and the mursal is more correct. And Allah knows best.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 240