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Ioannes Antonescu Res apud Vicidata repertae: Nativitas : 2 Iunii 1882 ; Pitești Obitus : 1 Iunii 1946 ; Jilava Patria : Romania Officium Officium : Prime Minister of Romania , Chief of the Romanian General Staff Munus : Politicus , military personnel , Legatus Consociatio Factio : Cohors Ferrica Familia Coniunx : Maria Antonescu Memoria Laurae : Knight's Cross of the Iron Cross , Order of Michael the Brave , Order of the German Eagle , Grand Cross of the White Rose of Finland Ioannes (Dacoromanice Ion ) Antonescu (natus die 15 Iunii 1882 in Piteşti, mortuus die 1 Iunii 1946 in Jilava) fuit primus minister et dictator ( conducător 'dux') Romaniae secundo bello mundano a die 4 Septembris 1940 usque ad diem 23 Augusti 1944, cum Romania foederata cum Germania Adolphi Hitler et Italia Beniti Mussolini erat. Postea ad mortem damnatus et in carcere Jilava supplicio affectus est. Bibliographia | Jean Ancel, Transnistria, 1941-194

Michael (rex Romaniae) Res apud Vicidata repertae: Nativitas : 25 Octobris 1921 ; Sinaia , Foișor Castle Obitus : 5 Decembris 2017 ; Aubonne Patria : Kingdom of Romania Officium Officium : member of the Senate of Romania Munus : Monarcha , Politicus Consociatio Religio : Ecclesia Orthodoxa Dacoromanica , Orthodox Christianity Familia Genitores : Carolus II ; Helena Coniunx : Anna Proles : Princess Sophie of Romania , Princess Elena of Romania , Princess Maria of Romania , Margaretha , Irina Walker Familia : House of Hohenzollern Memoria Laurae : Knight Grand Cross of the Royal Victorian Order , Chief Commander of the Legion of Merit , Order of the White Eagle , Order of Victory , Jubilee Medal "60 Years of Victory in the Great Patriotic War 1941–1945" , Legionnaire of Legion of Merit , Order of the Star of Romania , Order of Michael the Brave , Order of Faithful Service , Order of Carol I , Q1727291 , Order of the Crown , Iron Cross , Hou

Carolus II (rex Romaniae) Res apud Vicidata repertae: Nativitas : 15 Octobris 1893 ; Sinaia Obitus : 4 Aprilis 1953 ; Estoril Patria : Kingdom of Romania Officium Munus : sovereign Consociatio Religio : Ecclesia Orthodoxa Dacoromanica Familia Genitores : Ferdinandus I ; Maria Coniunx : Helena , Zizi Lambrino Proles : Michael , Carol Lambrino Familia : House of Hohenzollern Memoria Laurae : Order of the White Eagle , Order of the Star of Romania , Order of Michael the Brave , Order of St. Andrew , Order of Carol I , Q14900493 , Q1727291 , Order of Faithful Service , Order of the Most Holy Annunciation , knight grand cross of the order of the crown of italy , Knight Grand Cross of the Order of Saints Maurice and Lazarus , Ordo Periscelidis , Grand Cross with Star of the Virtuti Militari , Order of Saint Lazarus , Sash of the Three Orders , Order of the Star of Karađorđe , Royal Order of the Seraphim Sepultura : Curtea de Argeș Monastery Carol

1 $begingroup$ PT $(x-a_{1})(x-a_{2})..(x-a_{n})+1$ can not be factored into two smaller polynomial $P(x)$ and $Q(x)$ with integer coefficients, where $a_{i}$ 's are all different integers. This problem can be solved by considering the root of equation $P(x)Q(x)-1=0$ This problem comes from Terry Tao's book Solving mathematical problem (page 47), in which he gives a hint as if P(x) and Q(x) are such factors then what can you say about $P(x)-Q(x)$ How does one solve this problem this hint? Edit: This appears not to be true as pointed out by Darji and Eric. For interested readers, The actual problem can be found here, page 47 Excercise 3.7 polynomials contest-math irreducible-polynomials