# There is method to my madness

Find the sum of all $$p,q,s$$ such that

$$2^m.p^2+1=q^s$$

and $$p,q,s$$ are odd primes and $$m$$ is not divisible by 4.

Clarification:

For every such triple, add the values of $$p,q$$ and $$s$$ to obtain the answer.

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