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Number Theory Level pending

$$N+a^2+b^2$$ is a three digit number which is divisible by 5. $$a=10x+y$$ and $$b=10x+z$$, where $$z$$ is a prime number, and $$x$$ and $$y$$ are natural numbers. If $$a+b=31$$, then find the value of $$N.$$

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