OFFSET
1,2
COMMENTS
If a composite number C can be written in the form C = a^2+k*b^2, for some integers a and b, then every prime factor P (for C) being raised to an odd power can be written in the form P = c^2+k*d^2, for some integers c and d.
This statement is only true for k = 1, 2, 3.
For k = 7, with the exception of the prime factor 2, the statement mentioned above is true.
CROSSREFS
KEYWORD
nonn
AUTHOR
V. Raman, Sep 17 2012
STATUS
approved