## Sums of squares, cubes, and higher powers.(English)Zbl 0867.11066

Some problems concerning representability of integers as $$x^{k_1}+y^{k_2}+z^{k_3}$$ with $$1/k_1+1/k_2+ 1/k_3>1$$ are investigated experimentally, discussing questions of positivity of the variables as well. Lists of exceptions (i.e., numbers not represented) are obtained in several cases. For the case of sums of two squares and a ninth power, an infinite series of exceptions is exhibited.

### MSC:

 11P05 Waring’s problem and variants 11-04 Software, source code, etc. for problems pertaining to number theory

### Keywords:

sums of powers; generalized Waring problem
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### References:

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