Praise be to Allah.
Whoever catches up with the imam when he is bowing , and bows with him, that is regarded as a rak`ah for him, according to the view of the majority of scholars, even if he did not recite al-Fatihah. This is indicated by the report narrated by al-Bukhari (750) from Abu Bakrah, that he came to the Prophet (peace and blessings of Allah be upon him) when he was bowing and he bowed with him, before he reached the row. He mentioned that to the Prophet (peace and blessings of Allah be upon him) and he said: “May Allah make you more keen but do not do it again.”
It was narrated in a sahih report that Ibn Mas’ud (may Allah be pleased with him) said: “Whoever does not catch up with the imam when he is bowing has not caught up with that rak`ah.” (Narrated by al-Bayhaqi; classed as sahih by al-Albani in Irwa al-Ghalil, 2/262)
Ibn `Umar said: “Whoever catches up with the imam when he is bowing and bows before the imam raises his head, has caught up with that rak`ah.” (Narrated by al-Bayhaqi and classed as sahih by al-Albani, op. cit., 2/263)
Similar reports were narrated from Abu Bakr al-Siddiq, Zayd ibn Thabit and ‘Abd-Allah ibn al-Zubayr. (See Irwa al-Ghalil, 2/264)
Al-Nawawi (may Allah have mercy on him) said in al-Majmu’, 4/112:
“What we have mentioned about catching up with the rak`ah by catching up with ruku` (bowing) is the correct view, as stated by al-Shafi`i. It was also the view of the majority of our companions and the majority of scholars. It is the apparent meaning of the hadiths and all people are unanimously agreed upon it. There is another view, which is very weak, which suggests that it does not count.”
It says in ‘Awn al-Ma’bud (3/102):
“Note that the majority of imams are of the view that whoever catches up with the imam when he is bowing and joins him in the prayer is regarded as having caught up with that rak`ah, even if he did not recite anything. A group was of the view that whoever catches up with the imam when he is bowing has not caught up with that rak`ah. This was the view of Abu Hurayrah. Al-Bukhari narrated this concerning reciting behind the imam from all of those who were of the view that it is obligatory to recite behind the imam. This view was also favoured by Ibn Khuzaymah, al-Sibghi and other Shaf`i muhaddithin. Shaykh Taqiy al-Din al-Subki among the later scholars regarded this as a strong view, and al-Muqbili regarded it as more likely to be correct.”
The view that is more likely to be correct is the view of the majority, because of the hadiths and reports quoted above.
For more, please see these answers: 22344 , 6551 , 12601 , and 49037 .
And Allah knows best.