Should a traveller offer the prayers in shortened form in his house or pray in congregation in the mosque?

Prayer in congregation is obligatory and it is not
permissible for a Muslim not to do that unless he has an excuse. We have
already quoted the evidence for that from the Qur’aan and Sunnah. Please see
question no. 8918. 

Based on this, you have to offer the prayers in congregation
in the mosque. If the imam is a resident (is not travelling) then you should
offer the prayer in full with him, and not shorten it. 

Shaykh Ibn Baaz was asked: If a person travels to Jeddah, for
example, is he allowed to shorten his prayers or does he have to pray with
the congregation in the mosque? 

He replied: 

If the traveller is still en route, it does not matter, but
if he has reached his destination then he should not pray on his own, rather
he has to pray with the people and offer the prayer in full. But if he is
still on the road and is alone and the time for prayer comes, there is
nothing wrong with him praying on his own and shortening the prayers whilst
travelling, making the four-rakah prayers two rak’ahs. 

Majmoo Fataawa wa Maqaalaat Mutanawwi’iah li’l-Shaykh ‘Abd
al-‘Azeez ibn Baaz (12/297). 

Shaykh Ibn ‘Uthaymeen was asked: when and how should a
traveller pray? 

He replied: 

The traveller may pray two rak’ahs from when he leaves his
city or town, until he returns to it, because ‘Aa’ishah (may Allaah be
pleased with her) said: “When the prayer was first enjoined it was two
rak’ahs, then the prayer of the traveller remained like that but the prayer
of one who is not travelling was increased to four.” Narrated by
al-Bukhaari, 1090; Muslim, 685.  

And Anas (may Allaah be pleased with him) said: “We went out
with the Prophet (peace and blessings of Allaah be upon him) from
Madeenah to Makkah, and we prayed two rak’ahs each time, until we came back
to Madeenah. Narrated by al-Bukhaari, 1081; Muslim, 693.   

But if a traveller prays with an imam he should pray four
rak’ahs, whether he catches up with the prayer from the beginning or he
misses part of it, because the general meaning of the Prophet’s words: “When
you hear the iqaamah, then walk to the prayer, and you should be tranquil
and dignified, and not rush. Whatever you catch up with, pray, and whatever
you miss, complete it.” Narrated by al-Bukhaari, 636; Muslim, 602. The
general meaning of the phrase “Whatever you catch up with, pray, and
whatever you miss, complete it” includes travellers who pray behind an imam
who is offering a four-rak’ah prayer, and others. 

Ibn ‘Abbaas (may Allaah be pleased with him) was asked why a
traveller should pray two-rak’ahs when he is alone and four when he prays
behind a resident. He said: “That is the Sunnah.” Narrated by Muslim, 688;
Ahmad, 1865.  

The obligation to pray in congregation is not waived for the
traveller, because Allaah has enjoined that even in the case of fighting.
Allaah says (interpretation of the meaning): 

“When you (O Messenger
Muhammad) are among them, and lead them in As-Salaah (the prayer), let one
party of them stand up [in Salaah (prayer)] with you taking their arms with
them; when they finish their prostrations, let them take their positions in
the rear and let the other party come up which have not yet prayed, and let
them pray with you…”

[al-Nisa’ 4:102] 

Based on this, if the traveller is in a city or town other
than his own, he has to attend prayers in congregation in the mosque if he
hears the call to prayer, unless he is far away or fears that he may miss
meeting up with his travelling companions, because of the general meaning of
the evidence which indicates that the one who hears the adhaan or iqaamah is
obliged to pray in congregation. 

Majmoo’ Fataawa wa Rasaa’il al-Shaykh Ibn ‘Uthaymeen,
15/252. 

He was also asked: 

If I am travelling and I hear the call to prayer, do I have
to pray in the mosque? If I pray in the place where I am staying, is there
anything wrong with that? If the duration of my trip is more than four
consecutive days, should I shorten my prayers or offer them in full? 

He replied: If you hear the adhaan when you are in the place
where you are staying, then you have to attend the mosque, because the
Prophet (peace and blessings of Allaah be upon him) said to a man who
asked him for permission not to pray in congregation: “Can you hear the
call?” He said, “Yes.” He said: “Then answer it.” Narrated by Muslim, 6533.
And he (peace and blessings of Allaah be upon him) said:  “Whoever
hears the call and does not come, there is no prayer for him (i.e., his
prayer is not valid), except for one who has an excuse.” Narrated by
al-Tirmidhi, 217; classed as saheeh by al-Albaani in Saheeh al-Tirmidhi. 

There is no evidence to indicate that this ruling applies
only to the traveller, unless your going to the mosque will cause you some
problems in your journey, such as if you need to rest and sleep and you want
to pray in the place where you are staying so that you can sleep, or you are
afraid that if you go to the mosque the imam will delay the prayer, and you
want to leave and you are scared that you may miss the train or plane, etc. 

Majmoo’ Fataawa wa Rasaa’il al-Shaykh Ibn ‘Uthaymeen,
15/422.