## The number of powers of 2 in a representation of large even integers. I.(English)Zbl 1029.11049

Summary: Under the generalized Riemann hypothesis, it is proved that for any integer $$k\geq 770$$ there is $$N_k> 0$$ depending on $$k$$ only such that every even integer $$\geq N_k$$ is a sum of two odd prime numbers and $$k$$ powers of 2.
For Part II, see ibid. 41, 1255-1271 (1998; Zbl 0924.11086).

### MSC:

 11P32 Goldbach-type theorems; other additive questions involving primes 11N36 Applications of sieve methods 11P55 Applications of the Hardy-Littlewood method

### Keywords:

Goldbach problem; circle method; sieve method

Zbl 0924.11086
Full Text:

### References:

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