Let 
,
,
and 
denote positive integers satisfying
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(i.e., both pairs are relatively prime), and suppose every prime 
with 
is expressible if the form 
for some integers 
and 
. Then every prime 
such that 
and 
is expressible in the form 
for some integers 
and 
(Halter-Koch 1993, Williams 1991).
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