Problem
Problem of the Day #114
POTD April 1, 2024
Happy April Fools! This problem was inspired from China TST.
The numbers of sequences (a_1,...,a_{100}) whose terms are all nonnegative integers less than 97 such that 97 divides the sum of all the terms and the sum of the squares of all the terms can be written as a^b where \sqrt[n]{a} is not an integer for any n\ge 2. Find a+b.
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