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yeah, almost certainly yes, but no one has actually proved it in full.
the question is whether for every integer n greater than or equal to 2, four over n can be written as a sum of three positive unit fractions, meaning fractions of the form one over an integer.
this exact question is a famous open problem in number theory called the erdos straus conjecture (1948). its been around forever and somehow still open.
current status: no counterexample has ever been found. the statement is known to work for tons of cases, including all even n and many infinite families of odd n. on top of that, computers have brute-forced it for absolutely massive ranges of n (like up to 10^18), and it *always* works.
but despite all that evidence, there is still no general proof that it works for every single n. so mathematically speaking: everyone is basically convinced the answer is yes, but strictly speaking its still unproven. classic math moment tbh.
Actually we do find the concept of a divinely ordained exile in the Navi. Hashem does use the prophets to exhort the nation to indeed go to Bavel and those who didnt paid the price. Those who did were able to return with Ezra. You find verses referring to this in Melachim, Yirmeyahu, Yechezkel.
Mo’ed Katan 26a
Those who resisted Nebuchadnezzar’s exile are called:
“ממרים את פי הנביא” – those who rebel against the prophet’s word.
Sanhedrin 93a
The righteous who did submit to exile (like Daniel and his companions) are considered faithful to Hashem’s decree.Ramchal Maamar Hageula: ״וכדרך שֶׁהָיְתָה הַגָּלוּת, כָּךְ תִּהְיֶה הַגְּאֻלָּה. שֶׁהַגָּלוּת הָיְתָה תְּחִלָּה בַּפְּנִימִיּוּת וְאַחַר־כָּךְ בַּחוּצָה, וְכֵן הַגְּאֻלָּה תִּהְיֶה תְּחִלָּה בַּחוּצָה וְאַחַר כָּךְ בַּפְּנִימִיּוּת.”
another quote from Maamar HaGeulah describing the order of redemption
“ותחילת הגאולה היא התעוררות החיצוניות, שהוא קיבוץ הגלויות ושיבת ישראל לארצם… ואחר כך תבוא הגאולה הפנימית.”Otzrot Ramchal: “שיבת ישראל לארצם היא התחלת התיקון, שאז מתעורר הגוף של האומה, ואחר כך ישוב האור העליון להשלים את הנשמה.”
Adir Bamarom: “הבניין החיצון מקדים אל הבניין הפנימי, כי כך סדר הגאולה.”
Imagine the embarrassment that the neturei kartai will embrace when they are faced with the truth. Anyone who disagrees with the ramchal is a out of his mind.