5^ap^n=2^b+1
b=2m
2^b+1=(2^m+1)(2^m+1)-2^m+1
m+1=2s
(2^m+1+2^s)(2^m+1-2^s)
(2^2s-1+1+2^s)(2^2s-1+1-2^s)=5^ap^n
2^(2s-1)+2^s+1=p^n
2^(2s-1)-2^s+1=5^a
p^n-5^a=2^(s+1)
p^n+5^a=2^2s+2
p^n=2^s+2^(2s-1)+1
5^a=2^(2s-1)+1-2^s
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