A Note on Waring–Goldbach Problem: One Square, Four Cubes and One

Key Points

• This work aims to prove that large even integers can be expressed using specific combinations of prime powers.
• Establish representations of even integers as one square, four cubes, and one kth power of primes.
• Analyze exceptional cases and derive bounds based on the exponent ϑ(k).
• For k ≥ 4, almost all sufficiently large even integers n can be expressed as described, with O(N1/2 − ϑ(k) + ε) exceptions.
• The result improves upon previous findings by sharpening established bounds.