He wants evidence for the dhikrs that are said when bowing and prostrating

The dhikrs
that are said when bowing and prostrating are of three types: 

1-    
Some are common to both and are
said both when bowing and prostrating

2-    
Some are said only when bowing

3-    
Some are said only when
prostrating. 

The dhikrs
that are common to both include the following: 

“Subhaanaka
Allaahumma Rabbana wa bihamdika Allaahumma ighfir li (Glory and praise
be to you O Allaah, our Lord, O Allaah forgive me).” 

It was
narrated that ‘Aa’ishah (may Allaah be pleased with her) said: The Prophet
(peace and blessings of Allaah be upon him) often used to say when
bowing and prostrating: 

“Subhaanaka
Allaahumma Rabbana wa bihamdika Allaahumma ighfir li (Glory and praise
be to you O Allah, our Lord, O Allaah forgive me).”

Narrated by
al-Bukhaari (761) and Muslim (484). 

Another
dhikr that is common to both is “Subbooh Quddoos Rabb ul-malaa’ikati
wa’l-Rooh (Glorified, Holy, Lord of the angels and the Spirit)”. 

It was
narrated from ‘Aa’ishah that the Messenger of Allaah (peace and
blessings of Allaah be upon him) used to say when bowing and prostrating: “Subbooh
Quddoos Rabb ul-malaa’ikati wa’l-Rooh (Glorified, Holy, Lord of the
angels and the Spirit)”. Narrated by Muslim (487). 

Another
common dhikr is: “Subhaana dhi’l-jabarooti wa’l-malakooti wa’l-kibriya’
wa’l-‘azamah (Glory be to the One Who has all power, dominion,
magnificence and might).” 

It was
narrated that ‘Awf ibn Maalik al-Ashja’i said: I prayed qiyaam with the
Messenger of Allaah (peace and blessings of Allaah be upon him) one
night. He stood and recited Soorat al-Baqarah, and he did not come to any
verse that spoke of mercy but he paused and asked (for mercy). He did not
come to any verse that spoke of punishment but he paused and sought refuge
with Allaah.  Then he bowed for as long as he had stood, saying whilst
bowing: “Subhaana dhi’l-jabarooti wa’l-malakooti wa’l-kibriya’
wa’l-‘azamah (Glory be to the One Who has all power, dominion,
magnificence and might).” Then he prostrated for as long as he had stood,
and he said something similar when prostrating, then he stood and recited
Aal ‘Imraan, then he recited soorah by soorah. 

Narrated by
al-Nasaa’i (1132)and Abu Dawood (873). Classed as saheeh by Shaykh
al-Albaani in Saheeh Abi Dawood. 

Among the
dhikrs that are recited only in rukoo’ is: “Subhaana Rabbiy al-‘Azeem
(Glory be to my Lord the Almighty).” 

It was
narrated that Hudhayfah (may Allaah be pleased with him) said: I prayed with
the Prophet (peace and blessings of Allaah be upon him) one night, and
he started to recite al-Baqarah and I thought: he will bow when he reaches
one hundred, but he carried on. Then I thought that he would finish it in
the two rak’ahs, but he carried on. Then I thought he would bow after
finishing it, but he started to recite al-Nisa’ and recited it all, then he
started to recite Aal ‘Imraan and recited it all, reciting with a slow and
measured pace. When he reached a verse that spoke of glorifying Allaah, he
glorified Allaah; when he reached a verse that spoke of asking of Him, he
asked of Him; when he reached a verse that spoke of seeking refuge with Him,
he sought refuge with Him. Then he bowed and started saying, ‘Subhaana
Rabbiy al-‘Azeem (Glory be to my Lord the Almighty).” And his bowing was
almost as long as his standing. Then he said: “Sami’a Allaahu liman
hamidah (Allaah hears those who praise Him).” Then he stood for a long
time, almost as long as he had bowed. Then he prostrated and said, “Subhaan
Rabbiy al-A’la (Glory be to my Lord Most High),” and his prostration was
almost as long as his standing.

Narrated by
Muslim (772). 

Among the
dhikrs that are recited only when prostrating is: “Subhaana Rabbiy
al-A’la (Glory be to my Lord Most High).” 

In the
hadeeth of Hudhayfah quoted above it states that the Prophet (peace and
blessings of Allaah be upon him) used to say when prostrating: “Subhaana
Rabbiy al-A’la (Glory be to my Lord Most High).” 

Abu Dawood
(869) narrated that ‘Uqbah ibn ‘Aamir (may Allaah be pleased with him) said:
When the Messenger of Allaah (peace and blessings of Allaah be upon
him) bowed he said:  “Subhaana Rabbiy al-‘Azeem wa bi hamdihi (Glory
and praise be to my Lord the Almighty)” three times, and when he prostrated
he said: “Subhaana Rabbiy al-A’la wa bi hamdihi (Glory and praise be
to my Lord the Most High)” three times. 

The scholars
differed as to whether the additional phrase bi hamdihi (praise) is
saheeh or da’eef. The narrator of this phrase, Abu Dawood, said: We are
afraid that this phrase may not be sound; it was narrated only by the people
of Egypt. 

Shaykh
al-Albaani classed it as saheeh in Sifat al-Salaah (The Prophet’s
Prayer Described) p. 146, then later on he classed it as da’eef in Da’eef
Sunan Abi Dawood (1/338-340). 

It was also
rejected by Ibn al-Salaah and others, as stated in al-Talkhees al-Habeer
(1/243). 

Ibn Qudaamah
said in al-Mughni (1/297): Two reports are narrated from Imam Ahmad,
one which says that he accepted it and another which says that he did not
accept it. In the report that he did not accept it the reason give is the
fact that the hadeeth without this additional phrase is more well-known. 

Ahmad ibn
Hanbal was asked about it, according to a report narrated by Ibn al-Mundhir,
and he said: As for me, I do not say bi hamdihi. 

And Allaah
knows best.