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--- pow:problem5s25 [2025/04/15 01:32] – created mazur
+++ pow:problem5s25 [2025/04/18 13:25] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 85% round orange| Problem 5 (due Monday, April 14 )>
+A positive integer $N$ has the following properties:
+(1) $N$ is a square.
+(2) $N$ is the sum of two positive squares in a unique way (up to order).
+(3) $\text{d}(N)\phi(N)=8N$.
+(d(N) is the number of positive divisors of N and $\phi$ is the Euler function).
+What is N?
+</box>
+The answer is $N=2025$. I created the problem as a New Year puzzle to welcome the year 2025.
+We received solutions from  David Biddle, Raisha Chowdhury, Robert Kroplewski, Emily (Qingyue) Liu, Josiah Moltz.
+One solver submitted incorrect answer, another solver submitted a correct answer without justification that it
+is the unique possible answer. The other 3 solutions were complete and they are essentially the same as our
+in-house solution. For a detailed solution see the following link {{:pow:2025sproblem5.pdf|Solution}}.