feat(math): add inverse multiplicative function operations (#1867)

[morluto]

Summary

Implements the inverse_multiplicative domain with 3 atomic operations for computing inverse images of the Euler totient function.

Closes #1867

Operations

Operation	Description
number_theory.euler_phi.preimages.compute	Find all n with phi(n) = target
number_theory.euler_phi.preimage_count.compute	Count n with phi(n) = target
number_theory.euler_phi.preimage_power_sums.compute	Compute sum of n^k for phi(n) = target

Design

• Exact enumeration: All operations enumerate n in a bounded range [1, 4*target] and check phi(n) = target using exact integer arithmetic.
• Bounded range: The search range is bounded by 4*target, which is a known upper bound for solutions to phi(n) = target.
• No floating-point: All computations use exact integer arithmetic.

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[morluto]

Deep review summary

Verdict: REQUEST CHANGES — 4·target is not an upper bound for inverse totients, so all three operations return incomplete answers while claiming exact completeness.

The ratio n/φ(n)=∏_{p|n} p/(p-1) is unbounded as n acquires more small prime factors. A concrete small counterexample is

n = 2310 = 2·3·5·7·11
φ(n) = 480
4·480 = 1920 < 2310.

Therefore 2310 is a valid preimage of target 480, but every operation stops at 1920 and omits it. The returned preimage, count, and power sum are all false. There is no universal fixed constant C such that every solution of φ(n)=m satisfies n≤Cm.

Replace range scanning with a complete inverse-totient algorithm derived from

φ(p^a) = p^(a-1)(p-1),

recursively enumerating admissible prime powers whose totients divide the remaining target, with canonical duplicate elimination and a proof that the branch set is complete. Alternatively, expose an explicitly bounded search result that states the searched interval and never calls the result the full preimage.

The current runtime bound is also poor: for target 100000, it recomputes φ(n) by trial division for every n≤400000 separately. Even as a bounded scan, use one totient sieve, and have count/power-sum consume the same computed preimage rather than duplicate the search three times.

Add decisive regressions:

• target 480 must include 2310;
• every returned n must replay φ(n)=target;
• count and power sums must be exact projections of the same canonical preimage tuple;
• odd targets greater than 1 have empty preimage because φ(n) is even for n>2.