**Core Concept**
The patient's presentation is suggestive of a disorder of calcium and phosphorus metabolism, with primary hyperparathyroidism (PHPT) being a likely cause. PHPT is characterized by hypercalcemia due to excessive parathyroid hormone (PTH) secretion, which leads to increased bone resorption, renal phosphate excretion, and increased 1,25-dihydroxyvitamin D production.

**Why the Correct Answer is Right**
In PHPT, serum calcium levels are typically elevated, whereas in this case, the patient has low serum calcium. This discrepancy suggests that the patient may have a condition that mimics PHPT but with a different underlying cause. The elevated PTH levels are consistent with PHPT, but the low serum calcium levels point towards a different diagnosis. The correct investigation to establish a diagnosis in this case is one that can differentiate between PHPT and other conditions that cause similar biochemical abnormalities.

**Why Each Wrong Option is Incorrect**
**Option A:** Serum creatinine level is not directly relevant to the diagnosis of PHPT or the differential diagnosis in this case. While renal function may be affected in PHPT, serum creatinine is not a specific marker for this condition.

**Option B:** 24-hour urine calcium excretion is a useful test in PHPT, as it helps to differentiate between PHPT and other causes of hypercalcemia. However, in this case, the patient has low serum calcium, making this test less relevant.

**Option C:** Serum 1,25-dihydroxyvitamin D levels may be elevated in PHPT, but this test is not as sensitive or specific as other investigations, such as a parathyroid gland imaging study.

**Option D:** Serum magnesium levels are often low in PHPT, and this test can help to differentiate between PHPT and other causes of low serum calcium.

**Clinical Pearl / High-Yield Fact**
In patients with low serum calcium and elevated PTH, consider the possibility of pseudohypoparathyroidism type 1a, a genetic disorder characterized by resistance to PTH.

**Correct Answer: A. Serum creatinine level is the least contributory investigation in this scenario.