sum_of_squares_fortyone
plain-language theorem explainer
The integer 41 equals 4 squared plus 5 squared. Number theorists checking small cases of sums of two squares or primes congruent to 1 mod 4 would cite the identity for verification. The proof proceeds by direct numerical evaluation via the native decision procedure.
Claim. $41 = 4^2 + 5^2$
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. This theorem records a concrete numerical identity placed among the arithmetic-function definitions. No upstream lemmas are invoked.
proof idea
The proof is a one-line wrapper that applies the native_decide tactic to evaluate the equality by direct computation.
why it matters
The declaration supplies a verified instance of the sum-of-two-squares representation for the prime 41. It aligns with the classical theorem that primes congruent to 1 mod 4 admit such representations and can feed later arithmetic-function work in the module. No open questions are addressed.
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