Post B0p3VkmWWPHCTwZY8W by robinhouston@mathstodon.xyz
 (DIR) More posts by robinhouston@mathstodon.xyz
 (DIR) Post #B0p3VjudkkAtmpMW9I by rzeta0@mathstodon.xyz
       2025-12-02T00:35:20Z
       
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       The official solutions to the textbook I'm following says that prime 53 can't be expressed as the difference of two squares.Im confused.53=27²−26² Am I going mad? #maths #numbertheory
       
 (DIR) Post #B0p3VkmWWPHCTwZY8W by robinhouston@mathstodon.xyz
       2025-12-02T00:41:30Z
       
       0 likes, 0 repeats
       
       @rzeta0 What a peculiar mistake.
       
 (DIR) Post #B0p3VlY1fnH2rGnUB6 by robinhouston@mathstodon.xyz
       2025-12-02T00:43:41Z
       
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       @rzeta0 The next part doesn't make sense either. You can't write 3 as the sum of two squares, but e.g. 53 = 7² + 2².Does your book have a lot of mistakes, or is this page unusual?
       
 (DIR) Post #B0p3Vm6lad3yb13EKO by rzeta0@mathstodon.xyz
       2025-12-02T01:17:39Z
       
       0 likes, 0 repeats
       
       @robinhouston omg that is bad.I'm starting to lose trust in the textbook which is a shame because I found it the most easy to read and learn from compare to the famous and traditional textbooks which I find really difficult (Apostol, Andrews, Jones, etc)
       
 (DIR) Post #B0p3VmvoWptd9KvztY by shironeko@fedi.tesaguri.club
       2025-12-02T01:22:31.600792Z
       
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       @rzeta0 @robinhouston is this textbook originally in english? seems like both statements are exact opposite to the truth
       
 (DIR) Post #B0p7E3vR0TjiSXYmwq by robinhouston@mathstodon.xyz
       2025-12-02T02:01:32Z
       
       1 likes, 0 repeats
       
       @rzeta0 The truth is that an integer can be written as the difference of two squares iff it is not congruent to 2 modulo 4. Primality is irrelevant.This situation for sums of two squares is a bit more subtle and interesting: https://en.wikipedia.org/wiki/Sum_of_two_squares_theorem
       
 (DIR) Post #B0p7Gy0zRD8IztXlb6 by rzeta0@mathstodon.xyz
       2025-12-02T01:26:19Z
       
       1 likes, 0 repeats
       
       @shironeko @robinhouston This is the book, and the author is a professor at a UK university.https://global.oup.com/academic/product/number-theory-9780198846734?cc=gb&lang=en&I suspect the solutions were delegated to a student .....