Goldbach–Linnik type problems with one prime square and six prime cubes

Key Points

• This research aims to explore representations of odd integers using prime squares, cubes, and powers of 2.
• Demonstrated that for k1 ≥ 49, large odd integers can be expressed as prime square, six prime cubes, and k1 powers of 2.
• Proved that for k2 ≥ 73, pairs of large odd integers can form equations involving prime square, six prime cubes, and k2 powers of 2.
• Established that for k1 ≥ 49, any sufficiently large odd integer can be represented in the specified form.
• Confirmed that for k2 ≥ 73, every pair of sufficiently large odd integers satisfies the equation condition.