March 28, 2017

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Brilli the ant is considering the complexities of a 5-dimensional universe. She wants to count the number of integer points that are distance sqrt(n) away from the origin. Let Tn be the set of ordered 5-tuples of integers (a1,a2,a3,a4,a5) such that a1^2+a2^2+a3^2+a4^2+a5^2=n.However, being an ant, she doesn't have enough toes to record numbers that are above 10. Let Dn be the units digit of |Tn|.
Determine ∑ from 1 to 5678 of Di.

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