Abu Huraira (Allah be pleased with him) reported that the Messenger of Allah ﷺ forbade fasting on these two days. 'Id-ul-Adha and 'Id-ul-Fitr. (Using translation from Muslim 1138)  

«أَنَّ رَسُولَ اللَّهِ ﷺ نَهَى عَنْ صِيَامِ يَوْمَيْنِ يَوْمِ الْفِطْرِ وَيَوْمِ الْأَضْحَى»  

"The Messenger of Allah said: 'Fasting is a shield."' (Using translation from Nasāʾī 2224)   

قَالَ رَسُولُ اللَّهِ ﷺ «لَا صَوْمَ فِي يَوْمِ عِيدٍ» *  

[Machine] I witnessed the Eid with Umar ibn al-Khattab. He came, prayed, then turned and addressed the people, saying, "These are two days during which the Messenger of Allah ﷺ prohibited fasting: the day of your breaking the fast and the other day when you eat from your sacrifices."

Abu Ubaid said, "Then I witnessed the Eid with Uthman ibn Affan. He came, prayed, then turned and addressed the people, saying, 'Today, two Eids have coincided for you. Whoever from the residents of the higher areas wishes to wait for the Friday prayer, let him wait, and whoever wishes to return, let him return, for I have granted him permission.'

Abu Ubaid said, "Then I witnessed the Eid with Ali ibn Abi Talib while Uthman was present. He came, prayed, then turned and addressed the people."  

شَهِدْتُ الْعِيدَ مَعَ عُمَرَ بْنِ الْخَطَّابِ فَجَاءَ فَصَلَّى ثُمَّ انْصَرَفَ فَخَطَبَ النَّاسَ فَقَالَ «إِنَّ هَذَيْنِ يَوْمَانِ نَهَى رَسُولُ اللَّهِ ﷺ عَنْ صِيَامِهِمَا يَوْمُ فِطْرِكُمْ مِنْ صِيَامِكُمْ وَالْأَخَرُ يَوْمٌ تَأْكُلُونَ فِيهِ مِنْ نُسُكِكُمْ»

قَالَ أَبُو عُبَيْدٍ ثُمَّ شَهِدْتُ الْعِيدَ مَعَ عُثْمَانَ بْنِ عَفَّانَ فَجَاءَ فَصَلَّى ثُمَّ انْصَرَفَ فَخَطَبَ فَقَالَ إِنَّهُ قَدِ اجْتَمَعَ لَكُمْ فِي يَوْمِكُمْ هَذَا عِيدَانِ فَمَنْ أَحَبَّ مِنْ أَهْلِ الْعَالِيَةِ أَنْ يَنْتَظِرَ الْجُمُعَةَ فَلْيَنْتَظِرْهَا وَمَنْ أَحَبَّ أَنَّ يَرْجِعَ فَلْيَرْجِعْ فَقَدْ أَذِنْتُ لَهُ قَالَ أَبُو عُبَيْدٍ ثُمَّ شَهِدْتُ الْعِيدَ مَعَ عَلِيِّ بْنِ أَبِي طَالِبٍ وَعُثْمَانُ مَحْضُورٌ فَجَاءَ فَصَلَّى ثُمَّ انْصَرَفَ فَخَطَبَ النَّاسَ