Mathematics and Clergy

The Vicar and the Virger are standing in front of the church looking up at the West door, over which is inscribed the year when the church was built.

Vicar:- "It's funny, but that number is the sum of the squares of the ages of my cousin's two daughters"

Virger:-"I can't tell you their ages uniquely. Are they the same age?"

Vicar:-"If I was to tell you that, you'd be able to do the problem, so I'm not telling you."

Virger:-"Aha Vicar, now I know uniquely" and he tells the Vicar the ages of the cousin's two daughters.

When was the church built?

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credit David W Masser, Nottingham, 1970s.