x^{2} + y^{2} = 2013(u^{2} + v^{2})  (1) 
3(x_{1}^{2} + y_{1}^{2}) = 11·61(u^{2} + v^{2}),  (2) 
Now continue exactly as in part (b) using the prime 19, and contradict the minimality of x^{2} + y^{2}.
M = XY =  ( 

) 
 ∑_{n=1}^{∞}( 1)^{n}/q^{n}  1  = ∑_{n=1}^{∞}( 1)^{n}q^{n}/(1 q^{n})  
= ∑_{n=1}^{∞}∑_{k=1}^{∞}(q^{n})^{k}( 1)^{n+1}  
= ∑_{n=1}^{∞}( 1)^{n+1}q^{n}/(1 q^{n}),  
∑_{n=1}^{∞}1/(q^{n} + 1)  = ∑_{n=1}^{∞}q^{n}/(1 + q^{n})  
= ∑_{n=1}^{∞}∑_{k=1}^{∞}( 1)^{k+1}(q^{n})^{k}  
= ∑_{k=1}^{∞}( 1)^{k+1}q^{k}/(1 q^{k}). 
d /dx 1/(x^{n}  1)  = n/(x(x^{n/2} x^{n/2})^{2})  
d /dx 1/(x^{n} + 1)  = n/(x(x^{n/2} + x^{n/2})). 